FOR  PRIVATE  CIRCULATION  ONLY 


Investigation  of    some   Trouble 

in  the 

Generating  System 

of  the 

Commonwealth  Edison  Co. 

Chicago 


1919 


Charles  P.  Steinmetz,  A.  M.,  Ph.  D. 


Investigation  of    some   Trouble 


in  the 


Generating  System 


of  the 


Commonwealth  Edison  Co. 


Chicago 


1919 


Charles  P.  Steinmetz,  A.  M.,  Ph.  D. 


COPYRIGHT 

1910 
CHARLES  P.  STEINMETZ 


Schenectady,  N.  Y.,  December  19,  1919. 

Mr.  S.  Insull,  Pres. 
Commonwealth  Edison  Company, 
Chicago,  111. 

My  dear  Mr.  Insull: 

Enclosed  I  send  you  report  of  investigation  of.  some  operating  trou- 
bles in  the  generating  system  of  the  Commonwealth  Edison  Company, 
during  1919,  with  some  recommendations.  I  am  sending  copies  of  the 
report  to  Mr.  L.  Ferguson  and  to  Mr.  R.  F.  Schuchardt.  I  regret  that 
in  some  respects  the  report  is  not  as  final  and  conclusive  as  I  like  to 
see  it,  but  during  the  years  of  successful  operation  since  the  installation 
of  the  protective  reactances,  your  system  has  grown  and  changed  so 
much,  and  while  I  have  received  very  complete  and  extremely  satis- 
factory information  and  data  from  your  engineers,  it  necessarily  is  not 
possible  for  me  to  be  as  fully  familiar  with  the  system,  as  I  was  once, 
but  I  hope  that  I  shall  now  be  able  to  keep  in  closer  touch  with  it. 

Some  of  my  recommendations  therefore  are  more  general,  and  re- 
quire further  study  by  the  operating  engineers,  and  I  shall  be  glad  to 
co-operate  therein,  and  expect  to  be  in  Chicago  again  in  January.  More 
particularly  this  applies  to : — 

1.)  The  installation  of  power  limiting  reactors  between  the  North- 
west Station  and  Fisk  Street,  which  appears  to  me  extremely  desirable 
to  eliminate  the  excessive  interference  between  these  stations  in  case  of 
trouble  in  one  of  them.  As,  however,  the  tie  cables  between  these  sta- 
tions are  also  used  as  feeder  cables  for  intermediate  substations,  a  study 
by  your  engineers,  in  which  I  shall  be  glad  to  co-operate,  is  necessary 
to  devise  an  arrangement  of  installation  of  reactors,  which  would  not 
interfere  with  the  economic  use  of  tie  cables  of  substation  feeder  cables. 

2.)  The  substations  were  originally  operated  by  separate  feeders, 
but  the  need  of  using  the  feeder  cables  and  apparatus  in  the  most  eco- 
nomical manner  has  led  to  tying  substations  together  on  the  same 
feeder,  which  necessarily  increases  the  interference  between  substations 
and  between  generating  stations  in  case  of  trouble,  and  further  changes 
are  contemplated  and  desirable.  It  therefore  appears  advisable  to 
make  a  thorough  study  of  substation  operation  with  the  view  of  com- 
bining the  most  economical  use  of  cables  and  apparatus  with  the  mini- 
mum possibility  of  interference  between  stations  in  case  of  local  trou- 
ble. Such  study  can  be  made  only  by  the  operating  engineers  who  are 
fully  familiar  with  all  the  conditions,  but  I  shall  be  glad  to  co-operate 
in  it. 


One  suggestion  which  I  like  to  bring  to  your  consideration  is  that  of 
building  a  typical  model  of  your  system,  generating  stations,  cables  and 
substations,  perhaps  in  1/20,000  size.  We  have  done  that  for  a  number 
of  transmission  systems  and  while  your  system  is  far  larger  and  more 
complex,  I  believe  it  can  be  done  and  such  model,  operated  by  direct 
current,  may  be  contained  in  a  large  room,  and  while  not  all,  many 
operating  questions  could  be  studied  on  it  by  the  engineers,  and  the 
effect  of  various  disturbances  and  troubles  experimentally  investigated 
without  endangering  your  big  system. 

With  best  regards, 

Yours  very  truly, 

(Signed)  CHARLES  P.  STEINMETZ. 
CPS:R 


INVESTIGATION  OF  SOME  TROUBLE  IN  THE  GEN- 

ERATING  SYSTEM  OF  THE  COMMONWEALTH 

EDISON  CO.  OF  CHICAGO,  DURING  1919 

By  Charles  P.  Steinmetz,  A.M.,  Ph.D. 


I— RECOMMENDATIONS 

From  the  investigation,  the  following  recommendations  appear  to 
me  justified: 

1.)  To  reduce  the  liability  of  trouble,  by  carefully  going  over  all 
the  controlling  devices,  such  as  relays,  current  transformers,  circuit 
breaker- operating  mechanisms,  etc.,  especially  those  at  or  near  the  gen- 
erating stations  to  ascertain  whether  they  are  in  perfect  condition  and 
whether  they  are  of  the  most  reliable  and  safest  type  now  available, 
and  where  necessary  replace  them  or  change  them  to  the  safest  and 
most  reliable  now  available  for  the  existing  conditions  of  operation. 
It  must  be  expected,  that  during  the  time  which  many  of  the  controlling 
devices  have  been  in  operation  in  the  system,  advances  have  been  made 
in  type  and  design  of  circuit  controlling  devices.  The  conditions  of 
operation  have  become  more  severe,  due  to  the  increase  of  the  size 
of  the  system  and  especially  due  to  the  increasing  interconnection  of 
substations  by  tie  cables.  While  such  interconnection  materially 
increases  the  economy  in  the  use  of  the  cables,  it  also  increases  the 
severity  and  extent  of  local  troubles  such  as  short  circuits.  Further- 
more, many  of  the  controlling  devices  are  not  new  any  more. 

While  it  is  economically  not  feasible  to  replace  or  remodel  the  con- 
trolling devices  every  few  years  with  every  advance  of  the  art,  it 
probably  is  economically  feasible  to  do  so  with  regard  to  the  con- 
trolling devices  located  in  the  generating  stations  proper. 

2.)  To  study  the  possibility  of  intercepting  many  of  the  troubles  in 
their  beginning,  before  they  have  fully  developed  into  a  short  circuit. 
Cable  breakdowns  apparently  are  not  always  instantaneous,  but  often 


Report  of  Charles  P.  Steinmetz 


develop  gradually  within  a  time  from  a  few  seconds  to  many  days.  A 
sufficiently  sensitive  differential  relay  thus  may  discover  a  beginning 
cable  fault,  and  cut  off  the  cable,  before  the  fault  has  developed  into  a 
ground  or  short.  In  a  split  conductor  cable,  the  two  parts  of  each 
conductor  are  so  closely  identical,  that  a  very  sensitive  differential 
relay  can  be  placed  between  them,  and  as  a  fault  naturally  would 
develop  in  one  of  the  cable  halves  first,  the  relay  would  act  at  the 
very  beginning  of  the  fault.  The  possibilities  and  limitations,  and  in 
general  the  economic  feasibility  of  the  split  conductor  cable,  should 
thus  be  investigated.  Similar  results  are  given  by  grouping  in  pairs 
of  identical  cables  with  differential  relays  between  them.  This  latter 
arrangement  perhaps  is  somewhat  less  sensitive  and  reliable,  since  with 
two  separate  cables,  no  matter  how  identical  they  may  be,  a  transient 
may  occur  in  the  one  and  not — or  a  different  transient — in  the  other, 
and  the  sensitivity  of  the  differential  relay  thus  probably  has  to  be 
lowered  not  to  be  affected  by  transients.  On  the  other  hand,  the  latter 
arrangement  would  not  require  such  extensive  replacement  of  cables. 
Systems  involving  the  use  of  sheath  transformers  or  other  schemes  for 
tripping  out  on  small  ground  currents,  and  still  other  arrangements 
for  accomplishing  the  result  of  operating  on  an  incipient  fault,  should 
be  investigated. 

It  appears  that  some  cable  failures  are  preceded  by  a  gradual  de- 
crease of  the  insulation  resistance,  especially  while  hot,  extending  over 
many  days.  Such  failures  might  be  intercepted  by  a  systematic  testing 
of  the  cables  with  high  voltage  direct  current,  essentially  a  high  voltage 
resistance  measurement,  and  the  possibility  of  such  should  be  investi- 
gated. The  time  for  such  tests  should  be  chosen  immediately  after  the 
peak  loads  of  the  day,  when  the  cables  are  at  their  maximum  tempera- 
tures. I  understand  that  simple  devices  for  getting  high  voltage  direct 
current  for  testing  purposes  have  been  developed. 

3.)  To  cut  off  the  troubles  from  the  generating  stations  by  the  in- 
stallation of  feeder  reactances. 

By  far  the  largest  majority  of  troubles  leading  to  short  circuit  occur 
in  the  feeder  cables  and  beyond  them,  in  the  substations,  but  very  few 
only  in  the  generators,  and  extremely  few  on  the  busbars.  The  gen- 
erators have  power  limiting  reactors,  but  no  power  limiting  reactors 
are  used  in  the  feeders,  and  as  the  result,  any  short  circuit  in  a  feeder 
cable,  near  the  generating  station,  is  practically  a  short  circuit  on  the 
busbars,  that  is,  pulls  the  voltage  of  the  station  section  down  to  nothing, 
drops  out  the  synchronous  apparatus  and  thus  gives  serious  and  wide- 


Report  of  Charles  P.  Steinmetz 


spread  trouble.  Such  short  circuits  in  the  feeder  cable  near  the  gen- 
erating stations,  however,  may  be  expected  to  be  more  frequent  than 
short  circuits  in  the  generating  station  itself,  and  the  installation  of 
reliable  feeder  reactors  thus  would  eliminate  the  majority  of  short 
circuits  from  materially  affecting  the  generating  stations,  that  is,  from 
becoming  serious. 

I  would  recommend  that  0.9  ohm,  or  at  least  0.7  ohm  feeder  reactors 
(5.2%  to  4%  for  a  300  ampere  line)  be  installed,  and  the  circuit 
breakers  be  set  to  cut  off  as  quickly  as  possible,  in  case  of  a  short 
circuit  in  the  feeder.  I  believe  such  a  feeder  reactance  would  in  no 
way  adversely  affect  the  operation  of  the  substations,  but  it  would 
limit  the  short  circuit  to  about  100,000  KVA.  If  then  the  circuit 
breakers  can  be  made  to  open  this  short  in  less  than  a  second,  the 
station  voltage  will  be  only  a  little  affected  during  the  short,  due  to 
the  great  sluggishness  of  the  turbo-alternator  fields,  and  immediately 
come  back  to  practically  normal,  so  that  it  may  be  expected  that  no 
synchronous  apparatus  will  be  dropped  out,  that  is,  the  trouble  limited 
to  the  short  circuited  feeder  cable  and  its  substations.  If,  however,  the 
short  circuit  holds  on  for  several  seconds,  an  appreciable  voltage  drop 
must  be  expected  in  the  generating  stations,  and  at  least  some  of  the 
synchronous  apparatus  supplied  from  this  generating  station  would  be 
dropped  out. 

The  advantage  of  feeder  reactors  thus  not  merely  consists  in  limiting 
the  short  circuit  current  and  thereby  the  voltage  drop  and  in  general 
the  shock  on  the  system,  but,  by  permitting  to  set  the  circuit  breakers 
for  a  materially  shorter  time  limit,  it  also  greatly  reduces  the  duration 
of  such  short  circuit  and  thereby  correspondingly  reduces  the  liability 
of  dropping  synchronous  apparatus  and  spreading  the  trouble  beyond 
the  feeder  directly  involved. 

4.)  Install  a  power  limiting  busbar  reactance  between  the  two  sec- 
tions of  Fisk  Street  Station,  so  as  to  tie  the  three  station  sections :  Fisk 
Street  A,  Quarry  Street  and  Fisk  B,  together  into  a  ring.  This  should 
increase  the  synchronizing  power  between  these  stations.  It  should 
also  guard  against  the  system  being  cut  into  two  parts  out  of  synchron- 
ism with  each  other,  in  case  that  a  short  circuit  at  the  busbars  of  an 
intermediary  section  (Quarry  Street  or  Fisk  Street  B),  drops  the  volt- 
age of  this  section  to  zero  and  thereby  destroys  its  synchronizing  power. 

The  same  size  of  reactance  as  now  used,  of  about  1.75  ohms,  would 
be  recommended. 


4  Report  of  Charles  P.  Steinmetz 

5.)  I  should  recommend  strongly  to  endeavor  to  change  the  present 
connection  between  the  Northwest  Station  and  the  rest  of  the  system, 
which  now  consists  of  six  cables  to  Fisk  Street  B;  and  to  connect  the 
Northwest  Station  by  cables  and  power-limiting  reactances  to  Fisk 
Street  A,  as  well  as  Fisk  Street  B,  thus  making  a  second  ring,  between 
Fisk  Street  B,  Northwest  Station  and  Fisk  Street  A,  that  is,  have  the 
entire  system  of  four  station-sections  tied  together  into  a  double  ring, 
by  five  power  limiting  reactors. 

At  present,  due  to  the  absence  of  power  limiting  reactances  and  the 
low  resistance  (.3  ohms)  of  the  tie  cables  between  the  Northwest  Sta- 
tion and  Fisk  Street  B,  these  two  stations  are  practically  on  the  same 
busbars.  This  imposes  too  severe  a  duty  on  the  controlling  devices 
such  as  circuit  breakers,  of  these  two  stations,  and  a  trouble  in  one  of 
these  two  stations  is  equally  severe  in  the  other,  that  is,  a  short  circuit 
on  the  busbars  of  either  station  puts  both  stations  out  of  service  and 
thereby  involves  too  large  a  part  of  the  entire  system,  as  borne  out  by 
the  experience  of  September  18th. 

As  the  present  six  tie  cables  between  Northwest  Station  and  Fisk 
Street  B,  are  also  used  as,  feeder  cables  to  intermediary  substations,  in 
the  proposed  ring  connection  and  installation  of  reactances,  careful 
study  must  be  given  to  make  the  arrangement  such  as  not  to  interfere 
with  the  economical  use  of  these  tie  cables  as  feeder  cables  to  the  inter- 
mediary substations.  Possibly  three  (or  even  two)  of  these  cables  may 
be  used  between  Northwest  Station  and  Fisk  B;  three  (or  even  two) 
between  Northwest  Station  and  Fisk  A;  these  three  (or  two)  cables 
brought  together  at  the  station  end  to  a  short  auxiliary  bus  and  a  power 
limiting  reactance  installed  between  this  auxiliary  bus  and  the  main 
bus  of  the  station.  This  would  divide  the  power  limiting  reactance  into 
halves,  one  at  each  end,  thus  giving  a  total  of  four  new  reactances,  two 
at  the  Northwest  Station,  one  at  Fisk  A,  and  one  at  Fisk  B,  for  the 
interconnection  with  the  Northwest  Station.  Each  of  the  reactors  then 
would  be  about  .875  ohms  (half  the  size  of  the  present  power  limiting 
busbar  reactors) .  Such  an  arrangement  may  require  a  slight  increase 
of  excitation  of  the  synchronous  converters  in  the  substations  connected 
to  these  tie  cables,  to  keep  their  voltage  by  giving  the  current  a  slight 
lead.  Another  possibility,  which  might  be  more  convenient,  would  be 
to  install  normal  feeder  reactors  at  each  end  of  each  of  the  tie 
cables,  and  install  the  rest  of  the  required  reactance  in  the  substation, 
arranged  so  that  the  substation  or  the  individual  converters  in  the  sub- 
stations can  tap  the  feeder  cable  at  either  side  of  this  reactance,  de- 
pending on  from  which  station  it  intends  to  take  the  power.  That  is, 


Report  of  Charles  P.  Steinmetz  5 

two  busbars  may  be  used  in  the  substation,  connected  together  by  the 
power  limiting  reactance,  the  one  connected  to  the  one,  the  other  to  the 
other  generating  station,  and  the  converters  arranged  so  that  they  can 
be  thrown  on  either  of  the  two  busbars.  Possibly  a  still  better  arrange- 
ment may  be  devised. 

Until  reactors  are  installed  between  the  Northwest  Station  and  the 
rest  of  the  system,  I  would  recommend,  whenever  there  is  any  serious 
trouble  in  the  Northwest  Station,  or  in  Fisk  Street  B,  which  connects 
with  it,  to  immediately  open  all  the  tie  lines  between  these  two  stations, 
and  synchronizing  them  together  again  after  the  trouble  is  perfectly 
cleared. 

6.)  Install  in  each  station  section,  as  permanent  busbar  instruments, 
as  many  suitable  synchronoscopes  as  there  are  other  station  sections 
(three  at  present) ,  for  the  purpose  of  continually  indicating  the  phase 
difference  and  the  frequency  difference  of  the  station  section  from  all 
other  station  sections.  If  by  some  trouble  a  station  section  has  broken 
out  of  synchronism  with  the  rest  of  the  system,  it  appears  practically 
impossible  without  the  assistance  of  a  synchronoscope,  to  control  the 
steam  supply  in  this  station  section  so  as  to  have  it  promptly  drop  back 
into  synchronism.  With  a  synchronoscope,  however,  indicating  the 
speed  difference  of  the  station  from  the  next  adjoining  station,  with 
which  it  is  out  of  synchronism  (though  still  tied  with  it  by  the  react- 
ance), merely  the  ordinary  action  of  synchronizing  will  bring  the  sta- 
tion quickly  back  into  synchronism. 

Such  synchronoscope  would  also  indicate  the  phase  difference  be- 
tween adjoining  stations  due  to  the  power  flow  over  the  busbar  react- 
ances, and  thereby  permit  most  economical  load  control.  Such  syn- 
chronoscope would  be  very  valuable  in  case  of  trouble,  in  showing 
what  happens :  whether  the  stations  are  out  of  synchronism,  or  hunting 
against  each  other,  or  steady  but  with  excessive  power  flow  over  the  re- 
actors, etc.  It  is  possible  that  a  more  sensitive  type  of  synchronoscope 
will  have  to  be  designed,  than  the  present  one. 

7.)  For  the  present,  until  4,  5  and  6,  have  been  carried  out  I  would 
recommend,  in  case  the  voltage  of  a  station  section  disappears,  as  result 
of  a  short  circuit  at  or  near  the  station,  and  if  the  voltage  does  not 
promptly  come  back  after  the  clearing  of  the  short  circuit,  to  open 
the  power  limiting  reactor  or  reactors  which  connect  this  station  section 
with  the  rest  of  the  system,  and  thereby  isolate  it.  Then,  as  soon  as 
the  voltage  has  recovered,  the  isolated  station  should  again  be  syn- 
chronized in  with  the  rest  of  the  system.  If,  after  thus  isolating  the 


6  Report  of  Charles  P.  Steinmetz 

generating  station  in  which  the  trouble  has  occurred,  the  voltage  does 
not  promptly  recover,  it  means  that  the  individual  generators  of  this 
station  have  broken  out  of  synchronism,  and  the  quickest  way  of  restor- 
ing service  probably  is,  to  disconnect  the  generators  from  each  other, 
and  synchronize  them  again. 

8.)  A  special  study  should  be  made  of  the  method  of  operation 
of  the  substations,  that  is,  their  connection  to  the  generating  system 
and  to  each  other,  to  get  the  most  satisfactory  compromise  beween  re- 
liability and  economy;  that  is,  to  use  the  feeder  copper  most  econom- 
ically, and  at  the  same  time  in  case  of  trouble  reduce  to  a  minimum  the 
interference  of  the  substations  with  each  other,  and  of  the  generating 
station  sections  with  each  other  through  the  substations. 

The  question  then  requires  consideration,  whether  and  how  far  tie 
feeders  between  substations  are  to  be  used,  and  how  they  should  be 
controlled  and  protected.  Whether  every  important  substation  should 
receive  power  from  two  generating  station  sections,  and  whether  and 
what  protection  in  this  case  can  be  afforded  against  interference  be- 
tween the  two  substation  sections  in  case  of  trouble  in  any  generating 
station  section.  Or  whether  each  substation  should  be  fed  from  one 
generating  station  section  only,  but  adjacent  substations  connected  to 
different  generating  station  sections,  so  that  in  case  of  a  substation  shut- 
ting down  by  trouble  in  the  generating  section  feeding  it,  the  adjacent 
substation  can  maintain  service,  etc. 

Also,  the  question  of  the  control  of  the  converters  in  the  substations 
should  be  investigated,  whether  the  A.C.  circuit  breakers  might  be  set 
somewhat  higher;  whether  the  D.C.  reverse  current  relay  may  not  be 
given  a  time  limit  and  its  setting  increased;  whether  a  D.C.  power 
limiting  resistance  might  be  considered,  etc. 

Discussion  of  Recommendations 

While  recommendations  1)  to  3)  should  greatly  reduce  the  frequency 
of  troubles  or  keep  them  out  of  the  generating  system  by  isolating  or 
localizing  them  by  the  feeder  reactors,  it  obviously  is  not  possible  to 
absolutely  guard  against  the  occasional  troubles  in  the  generating  sys- 
tem, such  as  short  circuits.  But  as  soon  as  the  trouble  is  cleared  as  by 
the  opening  of  the  circuit  breakers,  in  a  second  or  a  few  seconds,  the 
system  should  immediately  return  to  normal,  and  to  begin  to  pick  up 
again  the  load  which  the  short  circuit  dropped.  The  most  serious 
feature  of  the  troubles  of  September  18th,  May  19th,  and  October  22nd, 
in  my  opinion,  was  that  with  the  clearing  of  the  short  circuit,  the  sys- 


Report  of  Charles  P.  Steinmetz 


tern  did  not  promptly  come  back  to  normal  voltage,  but  in  a  large  part 
of  the  system  (Fisk  Street  B  and  Northwest)  the  voltage  remained 
practically  zero  for  about  a  quarter  of  an  hour  after  the  trouble  had 
been  cleared.  It  appears,  as  the  result  of  the  momentary  short  circuit 
the  stations  had  broken  out  of  synchronism  with  each  other  and  were 
not  able  to  pull  back  into  synchronism,  but  kept  drifting  past  each 
other  indefinitely,  short  circuiting  each  other  and  thus  keeping  the 
voltage  down  to  practically  zero. 

In  these  very  large  power  systems,  it  is  essential  for  the  safety  of 
operation  to  limit  the  possible  local  concentration  of  power,  by  divid- 
ing the  system  by  power  limiting  reactors.  To  fulfill  their  purposes, 
these  reactors  must  be  fairly  large,  and  the  value  of  1.75  ohms  used 
in  the  power  limiting  busbar  reactors  of  the  Commonwealth  Edison 
Company  of  Chicago,  is  by  no  means  too  high.  Necessarily,  however, 
these  power  limiting  reactors  also  limit  the  synchronizing  power  be- 
tween the  station  sections.  Thus  if  in  a  station  section  as  Fisk  Street  A, 
which  is  connected  by  one  power  limiting  reactor  to  the  rest  of  the 
system,  full  load  of  60,000  KW  is  suddenly  thrown  off — as  by  a  short 
circuit  at  the  busbars  dropping  out  the  synchronous  machines  in  the 
substations — while  full  steam  supply  is  still  on,  the  synchronizing 
power  coming  over  the  power  limiting  reactor  is  insufficient  to  hold 
the  station  in  step,  and  the  station  breaks  synchronism  and  speeds  up. 
Whether  synchronous  operation  is  preserved  or  synchronism  broken, 
depends  on  the  relative  speed,  with  which  the  synchronous  machines  in 
the  substations  drop  out,  the  turbine  governors  shut  off  steam  and  the 
alternators  speed  up.  The  synchronous  machines  in  the  substations, 
carrying  load  on  the  direct  current  side  and  feeding  back  on  the  alter- 
nating side,  probably  would  drop  out  very  quickly,  while  the  turbine 
governors  must  take  an  appreciable  time  to  reduce  the  steam  supply, 
and  the  alternators  speed  up  rapidly;  at  full  voltage  and  full  steam 
supply,  a  little  over  a  second  after  the  load  has  dropped  off,  the  sta- 
tions would  have  speeded  up  so  as  to  have  broken  synchronism  with 
the  rest  of  the  system,  in  spite  of  the  maximum  synchronizing  power 
exerted  over  the  power  limiting  reactor.  In  reality  obviously  the  load 
cannot  drop  off  instantly  but  would  hold  on  an  appreciable  time,  and 
the  governors  would  immediately  begin  to  cut  off  steam;  but  on  the 
other  hand,  the  station  voltage  has  dropped  under  short  circuit,  and  is 
below  normal,  and  with  it  the  synchronizing  power  (which  goes  with 
the  square  of  the  voltage) .  Tying  the  station  section  by  power  limiting 
reactors  to  two  other  station  sections  (as  by  installing  a  reactor  between 
Fisk  Street  A  and  B,  thus  completing  ring  connection)  would  give 


8  Report  of  Charles  P.  Steinmetz 

ample  synchronizing  power,  at  full  voltage,  to  keep  the  station  section 
in  synchronism  with  the  rest  of  the  system,  even  at  no  load  but  full 
steam  supply,  so  that  it  could  break  out  of  synchronism  only  if  the 
short  circuit  lasts  sufficiently  long  to  demagnetize  the  alternator  fields 
and  thereby  drop  the  voltage. 

Therefore  it  is  recommended  to  tie  all  the  stations  by  power  limiting 
reactors  into  ring  connection. 

If  a  short  circuit  occurs  at  or  near  the  busbars  of  a  station  section, 
it  necessarily  drops  the  busbar  voltage  to  zero.  It  takes,  however,  a 
number  of  seconds  for  the  short  circuit  current  to  demagnetize  the 
alternator  fields,  and  if  therefore  the  short  circuit  is  opened  quickly, 
the  alternator  field  magnetism  is  still  there,  at  least  partly,  and  the 
station  voltage  thus  comes  back  instantly,  at  least  partly.  If  then  the 
station  section  has  sufficient  synchronizing  power  against  the  adjacent 
section,  it  is  probable  that  it  would  remain  in  synchronism,  no  further 
trouble  would  occur,  and  it  would  probably  catch  again  many  of  the 
synchronous  machines  receiving  power  from  it. 

If,  however,  the  short  circuit  lasts  long  enough  to  materially  demag- 
netize the  alternator  fields,  then  at  the  clearing  of  the  short,  the  voltage 
does  not  immediately  come  back,  as  the  field  magnetism  would  first 
have  to  build  up.  Without  voltage  there  obviously  can  be  no  synchron- 
izing power,  and  the  station  section  thus  probably  drifts  out  of  syn- 
chronism with  the  rest  of  the  system.  With  the  load  being  released  by 
the  dropping  out  of  the  synchronous  machines  in  the  substations,  before 
the  governors  can  cut  off  steam,  the  turbo-alternators  will  probably 
have  speeded  up  and  operated  their  emergency  steam  cut  off,  as  with 
full  steam  and  no  load  this  takes  only  about  ~L~y2  to  3  seconds.  The 
machines  then  slow  down  until  again  put  on  governor  control.  As 
there  are  necessarily  very  great  differences  between  the  individual  ma- 
chines in  the  speed  at  which  they  trip  the  excess  speed  cut  off,  in  the 
time  required  to  reach  this  speed,  and  in  the  rate  of  slowing  down,  it 
is  obvious  that  when  governor  control  is  restored,  the  individual  ma- 
chines and  the  station  section  as  a  whole  probably  are  far  from  syn- 
chronism with  the  rest  of  the  system.  It  therefore  is  hardly  to  be 
expected  that  they  would  promptly  drop  into  synchronism  but  rather 
would  continue  indefinitely  to  drift  out  of  synchronism  with  the  rest 
of  the  system. 

Two  alternators  or  stations,  thrown  together  out  of  synchronism, 
that  is,  differing  in  frequency  from  each  other,  will  promptly,  that  is, 
practically  instantly,  pull  each  other  into  step,  that  is,  the  slow  machine 


Report  of  Charles  P.  Steinmetz 


speeds  up  and  the  fast  machine  slows  down,  if  their  frequency  differ- 
ence was  low  enough.  This,  however,  would,  with  turbo-alternators, 
require  a  frequency  difference  not  much  exceeding  one  percent,  and  it 
is  not  probable  that  the  unloaded  station,  idling  on  the  governors, 
would  be  so  close  in  frequency  to  the  loaded  station,  especially  as  the 
frequency  difference  in  normal  steam  governing  of  these  turbo-alterna- 
tors is  4%  between  no  load  and  full  load.  If  the  frequency  difference 
is  greater,  the  two  stations  continue  drifting  past  each  other  out  of 
synchronism,  but  steadily  a  power  transfer  between  them  tends  to  pull 
them  nearer  together,  so  that,  even  with  an  initial  frequency  difference 
of  5%,  they  should  pull  each  other  into  synchronism,  in  about  a 
minute,  more  or  less.  However,  this  synchronizing  power  is  so  small, 
only  a  fraction  of  1%  of  the  rated  load,  and  much  less  than  the  exci- 
tation or  friction  and  windage  losses  in  the  machines,  so  that  the  in- 
evitable variations  in  the  steam  supply  when  governing  at  no  load, 
probably  are  much  larger  and  overshadow  this  synchronizing  power. 
That  is,  it  has  only  a  theoretical  interest,  and  practically  the  stations 
would  indefinitely  drift  past  each  other  out  of  synchronism;  with  the 
fluctuations  of  steam  supply,  etc.,  sometimes  coming  nearer  together, 
sometimes  drifting  farther  apart,  etc.,  until  at  some  time  they  happen 
to  drift  close  enough  together — within  \% — so  as  to  pull  each  other 
in  step. 

The  characteristic  of  this  drift  out  of  synchronism  is  that  the  fluctua- 
tions of  current,  etc.,  are  constant,  and  not  gradually  decreasing,  as  in 
hunting  oscillations,  and  the  frequency  or  period  of  fluctuation  is  ir- 
regular. This  seems  to  agree  with  the  observations. 

It  appears  then :  if  a  station  section  has  dropped  out  of  synchronism 
by  a  short  circuit  or  other  trouble,  as  indicated  by  its  voltage  not 
coming  back  promptly  at  the  clearing  of  the  short,  then  it  is  not  prob- 
able that  this  station  section  will  pull  itself  into  synchronism  within 
reasonable  time,  but  regular  synchronizing  appears  necessary. 

Either  the  reactor  or  reactors  connecting  this  station  section  should 
be  opened,  thus  isolating  this  station  and  allowing  it  to  again  build 
up  its  voltage,  and  then  it  should  be  synchronized  in  again  with  the 
rest  of  the  system. 

Or,  without  opening  the  reactors,  the  station  may  be  synchronized 
into  the  system  by  controlling  the  steam  supply  in  correspondence  with 
the  indications  of  synchronoscopes  connected  between  this  station  and 
the  adjacent  stations. 


10  *     Report  of  Charles  P.  Steinmetz 


Similar  drifting  past  each  other,  out  of  synchronism,  may  also 
occur,  as  the  result  of  a  disturbance  such  as  a  short  circuit,  between 
the  turbo-alternators  of  one  station,  especially  if  they  are  machines  of 
different  types,  as  in  the  Northwest  Station.  Or  a  single  machine  may 
break  out  of  synchronism,  while  the  other  machines  in  the  same  station 
stay  in  step — especially  if  the  off  machine  is  of  different  type,  as  No. 
11  in  Fisk  Street.  As  there  are  no  power  limiting  reactors  used  between 
the  machines  of  the  same  station,  the  quickest  way  of  restoring  syn- 
chronism would  probably  be,  in  the  first  case,  to  open  the  circuit  break- 
ers of  the  individual  machines  and  then  synchronize  them  again ;  in  the 
latter  case,  to  open  the  circuit  breakers  of  the  off  machine,  and  syn- 
chronize it  again. 

II— RECORD 

Four  troubles  were  studied,  occurring  respectively  on — 

September  18th,  1919,  3:47  P.M. 
September  18th,  1919,  5:27  P.M. 
October  22nd,  1919,  12:20  P.M. 
May  19th,  1919,  7:25  A.M. 

The  generating  system  is  divided  into  four  sections,  connected  in 
tandem,  with  the  A  section  of  Fisk  Street,  and  the  Northwest  Station  as 
the  two  ends  of  the  chain,  and  with  power  limiting  reactors  stated  to 
be  1.75  ohms  each,  between  Fisk  A  and  Quarry  Street,  and  between 
Quarry  Street  and  Fisk  B,  and  six  tie  cables  of  negligible  reactance 
and  about  .3  ohms  joint  resistance  between  Fisk  B  and  the  Northwest 
Station. 

1.)     Sept.  18th,  1919—3:47  P.  M. 

a)  A  short  circuit  close  to  the  busbars  of  B  section  of  Fisk  Street 
held  on  for  several  seconds,  before  it  was  opened. 

As  there  are  no  power  limiting  reactors  between  Fisk  B  and  North- 
west Station,  and  the  six  tie  cables  between  these  stations  are  of  very 
low  resistance,  the  Northwest  Station  was  just  as  seriously  affected  as 
Fisk  B,  and  indeed  acted  like  a  part  of  Fisk  B. 

b)  All  the  synchronous  machines  on  Fisk  Street  B,  and  on  North- 
west Station  dropped  out,  and  many  synchronous  machines  on  Fisk  A 
and  Quarry  Street:    44  synchronous  machines  on  Fisk  B  and  18  on 
Northwest  are  recorded  as  shut  down.     Of  26  machines  on  Fisk  A,  12 
dropped  out  and  14  stayed  in;   of  8  machines  on  Quarry  Street,  4 
dropped  out  and  4  stayed  in. 


Report  of  Charles  P.  Steinmetz  11 

c)  Due  to  the  voltage  dropping  to  zero  under  the  short  circuit,  the 
turbo-alternators  in  Fisk  B  and  Northwest  Station  dropped  out  of  syn- 
chronism with  each  other,  and  out  of  synchronism  with  Quarry  Street 
and  Fisk  A;  but  Quarry  Street  and  Fisk  A  remained  in  synchronism 
with  each  other. 

d)  Due  to  the  load  being  taken  off  by  the  dropping  out  of  syn- 
chronous machines,  the  turbo-alternators  in  Fisk  B  and  in  the  North- 
west Station  speeded  up  until  the  emergency  governors  tripped  the 
steam  valves.     The  turbo-alternators  were  put  back  on  the  governors 
immediately. 

e)  The  turbo-alternators  in  Fisk  B  and  in  Northwest  Station  did 
not  pull  into  step  with  each  other,  but  remained  out  of  synchronism; 
the  voltage  at  the  busbars  of  these  two  stations  remained  practically 
zero,  and  an  excessive  current  fed  into  Fisk  B  from  Quarry  Street, 
heating  the  power  limiting  reactor  B. 

f )  After  7  minutes,  the  tie  line  between  Fisk  Street  B  and  Quarry 
Street,  that  is,  the  power  limiting  reactor  B,  was  opened,  and  Quarry 
Street  and  Fisk  A,  came  back  to  normal.     About  the  same  time,  the 
30,000  KW  machine  in  Northwest  Station  began  to  lose  its  excitation, 
and  was  disconnected. 

g)  Fisk  B  and  Northwest  remained  out  of  synchronism  with  each 
other,  with  practically  zero  voltage  at  the  busbars,  for  six  minutes 
longer.    Then  the  voltage  suddenly  came  back,  the  alternators  in  Fisk 
B  pulling  into  synchronism  with  each  other  and  with  the  one  remaining 
(20,000  KW)  machine  in  Northwest. 

Remarks : 

a)  A  short  circuit  at  the  busbars  of  a  station  section,  pulling  the 
voltage  down  to  zero,  necessarily  must  drop  out  all  the  synchronous 
machines  on  this  section,  unless  the  short  circuit  is  opened  so  quickly, 
that  the  synchronous  machines  during  the  period  of  zero  voltage  did 
not  yet  drop  behind  by  half  a  pole,  but  at  the  reappearance  of  voltage 
are  still  in  step.    With  a  dead  short  this  would  usually  require  opening 
the  short  in  a  fraction  of  a  second. 

b)  The  purpose  of  sectionalizing  the  system  by  power   limiting 
reactors  was  to  limit  trouble  occurring  on  one  station  section  to  this 
section,  and  keep  it  from  affecting  the  other  sections. 

The  system  of  sectionalizing  therefore  has  not  worked  satisfactorily 
in  this  case,  as  all  the  synchronous  machines  in  Northwest,  and  nearly 


12  Report  of  Charles  P.  Steinmetz 


half  in  Fisk  A  and  Quarry  Street  have  dropped  out  due  to  the  trouble 
in  Fisk  B. 

There  is  no  power  limitation  between  the  Northwest  Station  and 
Fisk  B,  and  any  trouble  on  one  of  these  two  stations  thus  affects  the 
other  with  practically  the  same  severity.  This  is  undesirable,  as  thereby 
trouble  on  one  of  these  stations  affects  too  large  a  part  of  the  entire 
system.  It  is  dangerous,  as  Fisk  B  and  Northwest  combined  give  too 
large  a  power  for  safe  handling  under  all  emergencies.  Furthermore, 
due  to  the  connection  between  these  stations  being  practically  all 
resistance  and  no  reactance,  the  synchronizing  power  between  Fisk  B 
and  Northwest  must  be  small,  and  when  synchronism  is  once  lost  under 
short  circuit,  etc.,  trouble  must  be  anticipated  in  these  stations  pulling 
into  synchronism  with  each  other. 

The  interference  between  Fisk  A,  Quarry  Street  and  Fisk  B  sections — 
which  are  connected  with  each  other  by  power  limiting  reactors — re- 
sults in  serious  trouble  on  one  of  these  sections  dropping  out  numerous 
synchronous  machines  in  the  other  sections.  It  may  partly  be  direct 
interference  between  the  station  sections,  partly  through  substations 
fed  simultaneously  by  several  of  these  sections,  and  either  requires  fur- 
ther investigation. 

c)  If  the  busbar  voltage  of  a  station  section  drops  to  zero  by  short 
circuit,  for  a  sufficiently  long  time  to  permit  the  turbine  speeds  to 
change  appreciably,  this  station  section  is  out  of  synchronism  with 
the  rest  of  the  system,  as  at  short  circuit  of  zero  voltage  there  is  nothing 
to  hold  it  in  step.    As  soon,  however,  as  the  short  is  removed,  the  volt- 
age should  come  back  and  the  station  section  drop  into  step  again  with 
the  rest  of  the  system.    This  did  not  occur,  but  station  sections  remained 
out  of  step  with  each  other  at  practically  zero  voltage  for  a  considerable 
time,  about  a  quarter  of  an  hour.    Apparently,  the  synchronizing  power 
between  the  station  sections  is  lower  than  desirable,  and  the  speed  con- 
trol of  the  alternators  not  such  as  to  bring  them  promptly  so  close 
together  in  speed  as  to  drop  into  step. 

d)  The  tandem  or  chain  connection  of  the  stations  has  the  disad- 
vantage that  if  an  intermediary  station,  as  Fisk  B  or  Quarry  Street, 
even  momentarily  drops  out  of  synchronism  by  a  short  circuit,  the 
system  is  cut  in  two.     Ring  connection  of  the  station  sections  would 
have  the  advantage  that,  if  one  station  section  drops  out  of  step  by 
some  accident,  all  the  other  station  sections  are  still  connected  with 
each  other  and  thereby  can  remain  in  synchronism. 


Report  of  Charles  P.  Steinmetz  13 

2.)      Oct.  22nd,  1919—12:20  P.  M. 

The  trouble  was  very  similar  to  that  on  September  18th,  3:37  P.  M., 
a  short  circuit  close  to  the  busbar  of  Fisk  B,  except  that: 

a)  The  short  circuit  apparently  opened  very  quickly. 

b)  The  tie  lines  were  operated  manually,  separating  Fisk  B  and 
Northwest  stations. 

c)  Most  of  the  synchronous  machines  on  Fisk  B  and  Northwest, 
and  a  few  on  Fisk  A  and  Quarry  Street  dropped  out:    Of  52  synchron- 
ous machines  on  Fisk  B  and  Northwest,  46  are  recorded  as  dropped 
out,  six  as  remaining  in  synchronism;  of  6  machines  on  Quarry  Street, 
2,  and  of  35  machines  on  Fisk  A,  4  dropped  out,  the  remaining  stayed 
in  step. 

d)  In  Fisk  Street  B,  and  Northwest,  the  voltage  dropped  to  prac- 
tically zero,  but  came  back  at  the  opening  of  the  tie  line. 

Remarks: 

Apparently,  the  interference  between  the  stations  was  less  in  this 
case,  probably  due  to  the  short  duration  of  the  short  circuit,  and  the 
opening  of  the  tie  line  B,  so  that  only  few  synchronous  machines  fell 
out  in  the  other  sections,  and  some  even  stayed  in  step  in  the  disturbed 
section  if  the  report  is  correct. 

3.)     Sept.  18th,  1919—5:27  P.  M. 

a)  One  hour  forty  minutes  after  the  first  trouble,  resulting  from  a 
short  near  the  busbars  of  Fisk  B,  a  short  circuit  occurred  near  the 
busbar  of  Fisk  A,  and  held  for  several  seconds,  while  the  tie  line 
reactor  B  was  still  open,  that  is,  Fisk  B  and  Northwest  cut  off  from 
Quarry  Street  and  Fisk  A. 

b)  All  synchronous  machines  on  Fisk  A  dropped  out,  and  a  few 
on  Quarry  Street,  Fisk  B  and  Northwest;  39  synchronous  machines  on 
Fisk  A  are  recorded  as  having  dropped  out,  3  on  Quarry  Street,  5  on 
Fisk  B  and  1  on  Northwest. 

Remarks: 

a)  Some  synchronous  machines  dropped  out  on  Fisk  B  and  North- 
west, although  the  tie  line  between  these  stations  and  the  station  in 
which  the  trouble  occurred,  was  open,  showing  interference  between 
generating  stations  through  the  substations;  these  synchronous  ma- 
chines were  in  the  same  stations  with  machines  fed  from  Fisk  A  or 
Quarry  Street. 


14  Report  of  Charles  P.  Steinmetz 

b)  The  synchronous  machines  on  Fisk  B,  Northwest  and  Quarry 
Street,  which  dropped  out,  did  so  by  overload.  This  is  undesirable  as 
with  numerous  synchronous  machines,  fed  from  the  troubled  station  A, 
dropped  out,  those  which  receive  power  from  the  other  stations  should 
hold  on  to  carry  the  load. 

4.)     May  19th,  1919 — 7:25  A.  M. 

a)  A  generator  in  Fisk  Street  A  burned  out,  short  circuiting  with 
only  the  generator  power  limiting  reactance,  of  about  .4  ohms,  between 
the  short  and  the  busbars. 

b)  The  voltage  dropped  about  1,000  volts  in  all  four  station  sec- 
tions— a  little  more  in  Fisk  A,  where  the  trouble  occurred,  a  little  less 
in  Fisk  B  and  Northwest,  the  stations  most  remote  from  the  trouble. 

c)  A  violent  fluctuation  of  voltage  resulted  in  all  four  stations,  with 
an  amplitude  apparently  of  1,000  to  2,000  volts,  most  severe  in  Fisk  A, 
where  the  trouble  originated,  of  an  irregular  period  of  about  1  second 
per  beat. 

d)  The  tie  line  reactor  B,  got  very  hot. 

e)  The  drop  of  voltage  and  the  voltage  fluctuation  lasted  for  18 
minutes,  with  only  slight  decrease.     Then  they  suddenly  disappeared 
and  normal  voltage  returned. 

f)  During  the  disturbance,  the  frequency  of  the  system  fluctuated 
by  about  two  cycles,  that  is  8%,  and  three  machines  in  Fisk  A — where 
the  trouble  originated — tripped  their  excess  speed  governors  and  cut 
off  steam. 

g)  Some  synchronous  machines  dropped  out  of  step,  but  the  exact 
record  is  no  more  available. 

Remarks: 

a)  The  fluctuation  and  drop  of  voltage,  extending  over  all  four 
stations,  and  its  long  duration,  probably  were  of  similar  nature  and 
cause  as  the  loss  of  voltage  in  the  trouble  on  September  18th  and 
October  22nd. 

b)  The  most  serious  question,  which  unfortunately  cannot  be  de- 
cided with  the  present  data,  is :   whether  this  voltage  drop  and  fluctua- 
tion was  an  actual  hunting  of  the  generating  stations  against  each 
other,  due  to  lack  of  synchronizing  power,  or  whether  it  was  hunting 
of  the  steam  governors  of  the  stations  against  each  other,  or  whether 
it  was  only  apparent,  and  due  to  the  reaction  on  the  generators  of  the 
substations  when  starting  synchronous  machines.    This  should  be  fur- 
ther investigated. 


Report  of  Charles  P.  Steinmetz  15 

c)  It  appears  to  me  certain  that  in  this  case  the  generating  stations 
have  remained  in  synchronism  with  each  other  throughout  the  entire 
18  minutes  of  disturbance.    If  the  station  sections  had  dropped  out  of 
synchronism  with  each  other,  materially  greater  voltage  drops  should 
have  occurred. 

d)  The  observed  speed  fluctuation,  by  8%,  then  would  mean  that 
the  entire  system  simultaneously  speeded  up  and  slowed  down,  but 
not  that  material  speed  differences  existed  at  the  same  time  between 
different  turbines.    During  such  periodic  speed  pulsations,  temporarily 
some  machines  may  run  faster  than  others,  but  for  such  short  time 
only,  as  not  to  slip  out  of  synchronism.    As  the  observed  speed  fluctua- 
tion is  close  to  the  range,  for  which  the  excess  speed  governors  are  set, 
it  may  be  expected  that  some  machines  may  trip  their  emergency  cut 
off,  and  as  the  speed  fluctuation  may  be  expected  to  be  greatest  at  the 
source  of  disturbance,  Fisk  A,  the  tripping  out  may  be  expected  first  in 
Fisk  A,  as  was  observed;  3  machines  tripped  out  there. 

e)  Suppose  a  large  number  of  synchronous  machines  are  tripped 
out  by  a  momentary  short  circuit,  but  the  voltage  immediately  comes 
back  at  the  opening  of  the  short,  and  a  number  of  substations  immedi- 
ately proceed  to  start  their  synchronous  machines  from  the  alternating 
side.     Even  with  such  large  station  sections,  the  starting  of  several 
large  synchronous  machines  would  temporarily  pull  down  the  voltage. 
The  voltage  would  rapidly  recover  by  the  speeding  up  of  the  synchron- 
ous machines  which  had  been  started.     This  would  cause  some  other 
substations  to  start  their  synchronous  machines  and  again  pull  down 
the  voltage,  and  so  a  series  of  successive  voltage  drops  and  recoveries 
would  result  in  irregular  sequence,  until  the  last  synchronous  machine 
is  started.    This  would,  in  the  voltage  curve,  give  the  appearance  of  a 
hunting  pulsation,  such  as  shown  by  the  records.    This  theoretically  is 
a  possibility,  but  whether  it  was  the  cause,  cannot  be  decided  from  the 
records. 

Synchronoscopes  between  the  station  sections,  however,  would  indi- 
cate that  it  is  not  a  true  hunting,  due  to  instability  of  the  station 
sections,  but  a  voltage  fluctuation  due  to  excessive  fluctuating  lagging 
load,  as  given  by  the  starting  of  synchronous  machines. 

f)  Sufficiently  sensitive  synchronoscopes  between  the  station  sec- 
tions would  indicate  whether  the  station  sections  are  in  phase  with 
each  other  or  out  of  synchronism,  whether  they  are  hunting  against 
each  other,  and  whether  and  what  phase  displacement  exists  between 
the  station  sections. 


16  Report  of  Charles  P.  Steinmetz 

HI— OPERATION 
Momentum  of  Alternators 

The  emergency  steam  cut  off  s  of  the  turbo-alternators  are  stated  to 
he  set  for  an  excess  speed  of  about  10%. 

Considering  the  12,000  KW  units  typical  and  of  most  interest,  since 
most  of  the  units  in  Fisk  Street  where  the  trouble  originated  are  of  this 
size. 

An  increase  of  speed  of  10%  with  the  steam  valve  open  for  full  load, 
would  require  2  2/3  seconds.  With  the  steam  valve  opened  for  over- 
load, by  a  momentary  short  circuit,  the  speeding  up  to  the  speed  limit 
would  occur  still  more  rapidly.  The  ordinary  steam  governor  cannot 
well  be  made  to  act  quicker  than  this,  in  cutting  steam  off  completely, 
without  danger  of  steam  governor  hunting  interfering  with  the  stability 
of  the  system;  furthermore,  all  the  steam  in  turbine  and  the  passages 
beyond  the  valve  would  still  accelerate  it.  Thus  tripping  of  the  excess 
speed  emergency  steam  cut  off  may  be  expected  whenever  a  serious 
short  circuit  on  a  station  section  drops  out  all  the  synchronous  machines 
and  thereby  suddenly  relieves  the  load. 

Deceleration  tests  were  made  by  the  operating  engineers  on  four 
turbo-alternators,  with  excitation  and  without  excitation,  by  allowing 
the  machines  to  speed  up  on  the  throttle,  until  the  excess  speed  cut 
off  tripped,  and  then  observing  the  rate  of  slowing  down. 

The  observed  excess  speed  above  normal,  at  which  the  emergency 
cut  off  operated,  varied  from  6.7%  to  12%  with  the  different  machines, 
and  varied  by  as  much  as  1.3%  in  successive  tests  of  the  same  ma- 
chine. With  the  steam  valve  wide  open  during  acceleration,  an  appre- 
ciably higher  excess  speed  may  be  expected. 

The  rate  of  slowing  down,  after  the  steam  is  cut  off,  varied  from  4% 
to  13.4%  per  minute  at  no  excitation  and  from  6.75%  to  20.4%  per 
minute  with  the  field  excited. 

It  follows  herefrom:  suppose  by  a  short  circuit  lasting  an  appre- 
ciable time,  the  load  is  dropped,  and  the  turbo-alternators  speed  up 
and  trip  their  emergency  steam  valves  and  then  begin  to  slow  down. 
Then  the  individual  turbo-alternators  in  the  different  station  sections, 
and  even  in  the  same  station  section,  may  be  expected  to  differ  ma- 
terially from  each  other  in  speed,  probably  as  much  as  5  to  10%. 

With  such  great  differences  of  speed,  between  the  different  machines, 
diffiulties  in  synchronizing,  that  is,  in  the  machines  pulling  each  other 
into  step,  may  be  expected,  especially  between  different  station  sections. 


Report  of  Charles  P.  Steinmetz  17 

SYNCHRONIZING 
A 

If  two  alternators,  or  groups  of  alternators,  such  as  station  sections, 
are  connected  together  in  synchronism,  that  is,  at  the  same  speed,  but 
out  of  phase  with  each  other,  they  tend  to  pull  each  other  into  phase. 
The  machine  which  is  ahead  in  phase,  gives  off  power  and  thereby 
drops  back,  slows  down,  and  the  machine  which  is  behind  in  phase, 
receives  power  and  thereby  runs  ahead,  speeds  up,  and  as  the  result, 
when  the  two  machines  have  come  in  phase  with  each  other,  the  one 
which  was  ahead,  is  going  slower,  the  one  which  was  behind  is  going 
faster,  and  the  former  now  drops  behind,  the  latter  runs  ahead  in  phase, 
and  the  phase  difference  between  the  machine  reverses,  and  the  ma- 
chines thus  oscillate  against  each  other,  while  the  interchange  current 
between  the  machines  fluctuates  between  a  maximum  value  at  maximum 
phase  difference,  and  zero  or  a  minimum  value  when  machines  are  in 
phase.  If  there  were  no  damping  effects,  this  oscillation  would  con- 
tinue with  constant  amplitude.  Due  to  the  damping  effects  exerted  mainly 
by  the  lag  of  the  field  flux  behind  the  resultant  field  excitation  (the 
armature  reaction  component  of  the  synchronous  impedance),  the 
amplitude  of  the  oscillation  steadily  diminishes,  until  the  oscillation 
disappears.  That  is,  the  interchange  current  between  two  alternators 
which  are  in  synchronism  but  out  of  phase,  pulsates,  with  approximate- 
ly constant  frequency  of  the  beat,  but  with  an  amplitude,  which  grad- 
ually decreases  to  nothing. 

If  the  EMFs  of  the  two  machines  are  equal,  then  at  the  moment 
when  the  two  machines  are  in  phase,  there  is  no  resultant  EMF,  and 
thus  no  current,  and  when  the  machines  are  out  of  phase,  the  resultant 
EMF  is  approximately  in  quadrature  with  the  EMF  of  either  machine. 
If  then  the  circuit  between  the  two  machines  should  contain  only 
resistance  but  no  reactance,  the  interchange  current  between  the  two 
machines  would  be  in  phase  with  the  resultant  EMF,  thus  in  quadrature 
to  the  EMF  of  either  machine,  or  a  wattless  current  with  regards  to  the 
EMFs  of  the  machines,  that  is,  there  would  be  no  power  transfer  be- 
tween the  machines,  or  no  synchronizing  power.  If,  however,  in  the 
circuit  between  the  two  machines  the  resistance  is  negligible  compared 
with  the  reactance,  the  interchange  current  lags  (approximately),  90 
degrees  behind  the  resultant  EMF,  thus  is  in  phase  with  the  EMF  of  the 
one  machine,  in  opposition  with  that  of  the  other  machine,  thus  is  an 
energy  current  consuming  power  from  the  one  and  delivering  power 
to  the  other  machine.  Thus  only  the  reactive  component  of  the  inter- 
change current  between  two  alternators  which  are  in  synchronism  but 


18  Report  of  Charles  P.  Steinmetz 

out  of  phase,  transfers  power  between  the  alternators  and  is  synchron- 
izing current,  while  the  energy  component  of  the  interchange  current 
does  not  contribute  to  bring  the  machines  into  phase. 

If  the  EMFs  of  the  two  machines  are  unequal,  then  upon  the  power 
transferring  or  synchronizing  current  due  to  the  phase  difference,  super- 
poses a  reactive  current  which  magnetizes  the  machine  of  lower  voltage 
and  thereby  raises  its  voltage,  and  demagnetizes  the  machine  of  higher 
voltage  and  thereby  lowers  its  voltage,  but  does  not  transfer  power  be- 
tween the  machines  and  does  not  appreciably  change  the  phenomena 
of  power  transfer  by  the  synchronizing  current,  so  that  here  and  in  the 
following,  where  we  are  mainly  interested  in  the  magnitude  of  the 
effects,  we  may  for  simplicity  assume  equality  of  EMF  of  the  machines. 

B 

If  two  alternators  or  groups  of  alternators  such  as  station  sections, 
are  connected  together  out  of  synchronism,  that  is  while  differing  from 
each  other  in  frequency,  they  slowly  slip  past  each  other,  and  during 
each  cycle  of  slip,  or  beat,  a  periodic  energy  transfer  takes  place,  while 
the  interchange  current  periodically  rises  and  falls.  During  one-quar- 
ter the  cycle  of  slip,  or  beat,  the  alternators  are  partly  in  phase  with 
each  other,  that  is,  their  EMFs  are  in  the  same  direction.  The  slower 
machine  then  receives  energy  and  accelerates,  the  faster  machine  gives 
off  energy  and  slows  down  and  the  two  machines  thus  are  brought 
nearer  to  each  other  in  speed,  pulled  towards  synchronism.  During 
the  next  quarter  cycle  of  speed,  however,  the  alternators  are  partly  in 
opposition,  that  is  their  EMFs  are  in  opposite  directions.  The  faster 
machine  then  receives  energy  and  speeds  up,  the  slower  machine  gives 
off  energy  and  slows  down,  and  the  two  machines  pull  apart  again,  by 
the  same  amount  by  which  they  pulled  together  in  the  preceding 
quarter  cycle  of  slip.  Thus  the  machines  can  pull  into  step  only  if 
the  energy  transferred  during  one-quarter  cycle  of  slip  is  sufficient  to 
bring  them  into  step,  that  is,  is  larger  than  the  energy  required  to 
speed  the  momentum  of  the  slower  machine  up  to  synchronous  speed 
(or  slow  down  the  momentum  of  the  faster  machine  to  synchronism) . 
This  gives  the  maximum  value  of  slip  from  synchronism,  at  which  the 
machines  will  promptly  pull  into  step,  or  the  limits  of  synchronizing 
power. 

c 

If,  however,  the  two  machines,  or  station  sections,  are  out  of  syn- 
chronism with  each  other  by  a  greater  speed  difference  than  that  from 
which  they  can  pull  each  other  into  step  in  one-quarter  cycle  of  slip, 


Report  of  Charles  P.  Steinmetz  19 

and  if  the  machine  voltage  were  perfectly  constant,  then  the  machines 
would  never  come  into  synchronism,  but  would  continue  indefinitely 
to  slip  past  each  other,  coming  nearer  together  during  the  one-quarter 
cycle  of  slip  where  their  voltages  are  in  the  same  direction,  and  drifting 
apart  again  by  the  same  amount  during  the  next  quarter  cycle  of  slip, 
where  their  voltages  are  in  opposition.  In  reality,  however,  the  EMF 
of  the  machines  is  not  constant,  but  must  vary  periodically  with  the 
frequency  of  the  current  fluctuations,  that  is,  twice  the  frequency  of 
the  slip.  The  current  in  the  circuit  between  the  two  alternators  pul- 
sates, between  large  values  during  the  quarter  cycle  of  slip,  when  the 
EMFs  of  the  alternators  are  in  opposition,  and  small  values  during 
the  next  quarter  cycle  of  slip,  when  the  EMFs  are  in  the  same  direction, 
and  with  it  varies  the  armature  reaction.  The  phase  difference  between 
the  resultant  current,  and  the  EMF  of  each  alternator  periodically 
changes  from  0  to  360  degrees,  during  each  cycle  of  slip.  With  the 
periodic  fluctuation  of  the  current  and  its  phase  angle,  the  armature 
reaction  of  the  machine  fluctuates,  and  thereby  gives  a  periodic  fluc- 
tuation of  voltage.  As,  however,  the  armature  reaction  requires  an 
appreciable  time  to  develop,  the  voltage  fluctuation  is  not  in  phase 
with  the  fluctuating  current,  but  lags  behind  it,  by  an  angle  depending 
on  the  time  required  for  the  armature  reaction  to  exert  its  magnetizing 
effect.  The  result  thereof  is  that  the  power  interchange  between  the 
two  alternators  is  not  entirely  alternating  with  the  frequency  of  the 
slip,  that  is,  alternately  accelerating  each  machine  and  then  again 
slowing  it  down  by  the  same  amount,  but  has  a  constant  though  small 
component,  which  is  positive,  that  is,  accelerating  in  the  slower,  and 
negative,  that  is  retarding,  in  the  faster  machine.  This  represents  a 
continuous  synchronizing  power,  which  steadily  pulls  the  machines 
together  in  speed,  until  their  speed  difference  has  become  small  enough 
to  pull  suddenly  into  step. 

If  thus  two  alternators,  or  station  sections,  are  out  of  synchronism 
with  each  other  by  so  great  a  frequency  difference,  that  they  cannot 
pull  each  other  into  step  within  one-quarter  cycle  of  slip,  then  the 
alternators  continue  slipping  past  each  other,  with  large  fluctuating 
currents  flowing  between  them.  These  current  fluctuations — and  the 
voltage  fluctuations  caused  by  them — do  not  decrease  (as  in  hunting 
or  in  other  synchronous  oscillations),  but  remain  practically  constant 
in  amplitude,  but  the  fluctuations  gradually  become  slower,  that  is,  the 
frequency  of  beats  decreases,  while  the  machines  pull  nearer  together 
in  frequency,  that  is,  their  speed  difference  decreases,  until  the  critical 
speed  difference  is  reached,  where  the  acceleration  during  one-quarter 


20  Report  of  Charles  P.  Steinmetz 

cycle  of  slip  brings  the  machine  up  to  full  synchronism.  Then  sud- 
denly the  machines  drop  into  step  with  each  other,  the  excess  current 
vanishes  and  normal  voltage  comes  back,  after  a  short  oscillation  of 
constant  frequency  of  beats,  but  rapidly  decreasing  amplitude. 

Apparently,  this  is  what  happened  in  the  trouble  on  September  18th, 
1919. 


If  two  alternators  or  groups  of  alternators  such  as  station  sections, 
are  connected  to  each  other  through  a  reactance,  and  the  driving  power 
of  each  group  of  alternators  equals  its  load  (plus  losses),  then  no  cur- 
rent and  no  power  flows  over  the  dividing  reactor,  and  both  alternators 
are  in  phase.  If  now,  with  the  same  load,  the  driving  power  on  one 
alternator  is  increased,  on  the  other  decreased,  or  with  the  same  driving 
power,  the  load  on  the  one  is  increased,  on  the  other  decreased,  but 
the  terminal  voltage  kept  the  same,  then  current  and  power  flows  over 
the  dividing  reactor,  resulting  in  a  phase  displacement  between  the  two 
alternators  (or  station  sections).  This  phase  displacement  increases 
with  the  increase  of  power  transfer.  This  gives  a  case  where  current 
and  power  is  carried  over  a  reactance  from  one  circuit  to  another  one, 
without  any  voltage  drop.  It  is  this,  on  which  the  use  of  limiting 
busbar  reactors  is  based.  The  power  transfer  reaches  a  maximum  at 
90  degrees  phase  displacement;  this  gives  the  limits  of  synchronizing 
power,  and  any  further  increase  of  power  transfer  causes  the  two  alter- 
nators to  drop  out  of  synchronism  with  each  other. 

Too  large  reactance  between  the  alternators  reduces  the  synchroniz- 
ing power  by  limiting  the  synchronizing  current;  too  small  reactance 
may  again  reduce  the  maximum  synchronizing  power  by  lowering  the 
EMF  by  the  large  voltage  drop  due  to  the  large  interchange  currents. 
With  a  capacity  of  about  60,000  KW  per  station  section  and  machines 
of  the  general  characteristics  of  those  involved  (100%  synchronous 
reactance,  \2^/^%  true  reactance,  in  average) ,  maximum  synchronizing 
power  would  require  a  reactance  between  each  station  section  and  the 
rest  of  the  system  of  a  little  less  than  one  ohm,  so  that  the  proposed 
arrangement  of  ring  connection  of  the  stations  through  power  limiting 
reactors  of  1.75  ohms  should  give  about  the  maximum  synchronizing 
power. 


Mathematical  and  numerical  data  pertaining  to  the  preceding  are 
given  in  the  Appendix. 


Appendix 


22  Report  of  Charles  P.  Steinmetz 

APPENDIX 

Synchronous  Operation 
A 

Consider  the  case  of  two  alternators  or  groups  of  alternators 
such  as  station  sections,  which  are  running  in  synchronism  with  each 
other,  that  is,  have  the  same  frequency  f,  but  are  connected  together 
while  out  of  phase  with  each  other  by  angle  2w.  That  is,  the  one 
alternator  has  the  voltage  phase  (<f>—  to),  the  other  the  voltage 
phase  (0+w). 

We  may  assume  the  alternators  as  of  equal  voltage,  since  a 
voltage  difference  superposes  on  the  synchronizing  energy  current 
due  to  the  phase  difference,  a  reactive  magnetizing  current  due  to 
the  voltage  difference  without  materially  changing  the  energy 
relations. 

The  EMFs  of  the  two  alternators  then  may  be  represented  by: 

ei  =  E  cos  (0  —  co)  1 

e2  =  Ecos  (0+co)  /  (1) 

and  the  resultant  voltage  in  the  circuit  between  the  alternators  then  is : 
e  =  ei  — e2 

=  E  cos  \  (<f>  —  co)  —cos  (</>+  co)  [ 

=  2E  sin  co  sin  0  (2) 

and  the  interchange  currentwbeteen  the  alternators  is: 

2E    . 

i  =  —  sin  co  sin  (<j>  —  a) 

(3) 
where: 

z  =  r2+x2 

is  the  impedance  of  the  circuit  between  the  two  alternators,  and  the 
phase  angle  a  is  given  by: 

x 

tan  a  =  - 

r 

and: 

r= resistance 
x  =  reactance 

of  the  circuit  between   the   alternators    (including   their  internal 
resistances  and  reactances). 


Report  of  Charles  P.  Steinmetz  23 

The  power  of  one  of  the  two  alternators  then  is  given  by: 

2E2 

= sin  co  sin  (d>  —  a)  cos  (<f>  —  co) 

z 

E2  f  1 

=  —  sin  co  sin  { (20  —  a—  co)+sin  (co  —  cm 

Z  I  J 

E2  E2  E2 

=  —  sin  co  sin  (2<f>— a—  0))+^-  cos  a—  jr-  cos  (2co  — a)  (4) 

»  ^7  ^7 

The  phase  angle  co  of  the  EMF  is  not  constant,  but  pulsates  with 
approximately  constant  low  frequency,  the  frequency  of  the  beat, 
and  decreasing  amplitude. 

co0=co0oe  =  maximum  value  of  the  phase  angle,  then  may 
approximately  represent  the — gradually  decreasing — amplitude  of 
the  phase  angle,  where  a  =  attenuation  of  the  beat  or  oscillation,  and 

-at  .  ... 

co=a>oo«        sin  pc/>  (5; 

would  approximately  represent  the  instantaneous  value  of  the  phase 
angle  co  where: 

pf=  frequency  of  the  beat,  or  the  periodic  variation  of  the  phase 
angle. 

[In  the  derivation  of  equations  (3)  and  (4),  co  has  been  assumed 
as  constant.  As  co  is  not  constant,  but  by  (5)  a  function  of  <£,  addi- 
tional terms  appear  in  equations  (3)  and  (4).  Since,  however,  the 
frequency  of  variation  of  co  is  very  low  compared  with  the  frequency 
of  <j> :  p  =  a  small  quantity ;  these  additional  terms  in  (3)  and  (4)  are 
small,  and  equations  (3)  and  (4)  are  correct  with  sufficient  approxima- 
tion, especially  in  the  present  case,  where  we  are  essentially  interested 
in  the  magnitude  of  the  power  relations.] 

In  equation  (4),  the  first  term: 

E2   . 

Pi  — —  sin  co  sin  (2c>  — a— co) 

is  of  double  the  frequency  2f.  It  thus  does  not  represent  energy 
transfer  between  the  two  alternators,  but  merely  represents  the 
energy  storage  and  return,  twice  per  cycle,  occurring  in  any  inductive 
circuit.  It  thus  is  of  no  further  interest. 

The  second  term 
p"i=«-  cos  a 


24  Report  of  Charles  P.  Steinmetz 


gives,  substituting  cos  a  =  - ; 

z 


E2g 
P"i=2?       2 

where  g  is  the  conductance  of  the  circuit.  That  is,  this  term  is  the 
energy  loss  in  the  conductance,  that  is,  the  resistance  of  the  circuit, 
and  thus  also  is  of  no  further  interest. 

The  third  term: 

p'Y=-!|cos(2a>-a) 

is  of  the  low  frequency  of  the  beat,  or  the  current  fluctuation  between 
the  two  alternators:     pf.     It  thus  represents  the  energy  transfer 
between  the  two  alternators,  during  their  periodic  oscillations, 
or,  resolving  the  last  equation: 

E2  E2 

p'Y=  —  TT  sin  a  sin  2a>  —  =-  cos  a  cos  w. 
2z  2z 

The  second  term: 

E2 

p'Y'=  —  «-  cos  a.  cos  a> 

has  the  same  sign  for  negative  w,  that  is,  when  the  machine  is  lagging, 
as  for  positive  w  when  the  machine  is  leading,  thus  it  represents  no 
energy  transfer  between  the  machines. 

The  synchronizing  power,  or  energy  transfer  during  the  synchro- 
nizing oscillations  of  two  alternators,  which  are  out  of  phase  but  in 
synchronism,  thus  is  given  by  the  expression: 

E2 

P=«-  sin  a  sin  2co  (6) 

Thus,  the  synchronizing  power  p,  is  a  maximum,  and  is : 
_E2   . 

for  a  =  90  degrees,  that  is,  if  the  resistance  r  of  the  circuit  between 
the  alternators  is  negligible  compared  with  the  reactance. 

The  synchronizing  power  p  =  0  for  a  =  0,  that  is,  in  the  (theoretical) 
case,  when  the  circuit  between  the  alternators  contains  no  reactance, 
but  only  resistance. 

For  phase  angles  w  up  to  45  degrees,  that  is,  phase  displacements 
between  the  two  alternators  up  to  2  w  =  90  degrees,  the  synchronizing 
power  increases ;  beyond  this  it  decreases  again  and  becomes  zero  for 
2w=180  degrees  phase  displacement. 


Report  of  Charles  P.  Steinmetz  25 

The  average  value  of  p  may  be  approximated  by: 

E2    .       2  (l-cos2a>0)      E2   . 
avg.  p=^r  sin  a  —  -  --  -  =  -  sin  a  (1  —  cos  2a>0) 

2Z  7T   COo  7TCOZ 

where  coo  denotes  the  maximum  value  of  co 

and  as  the  duration  of  one  half  cycle  of  oscillation  —  during  which  the 
power  transfer  remains  in  the  same  direction  —  is  given  by  equation 
(5)  as: 

p$  =  27rpft  =  7r 

that  is, 

t==2p~f 

The  energy  transfer  between  the  two  machines,  during  each  half 
cycle  of  oscillation,  is  given  by: 

W  =        avg.  p.  (8) 


F2 

sin  a  (1  —  cos  2&>0) 


2  Trpf  cooZ 

in  this,  E  is  the  maximum  value  of  the  voltage  of  each  machine. 
Denoting  by : 

F    -E 

E°~72 

the  effective  value  of  the  machine  voltage,  gives  the  effective  values : 
Resultant  voltage: 

e°  =  2E0sinco  (21) 

Current: 

2F 

io=  — -  sin  w  (31) 

z 

Power  transfer: 

F  2 

p=  — —  sin  a  sin  2co  (6l) 

z 

Energy  transfer  during  each  half  cycle  of  oscillation  or  beat: 

W=  ^-sin  a  (1-cos  2  Wo)  (81) 

TrpfwoZ 

where : 

co=cooo€        sin  p<£  (5) 

is  the  angle  of  phase  displacement  of  either  machine,  from  the 
average ; 


26  Report  of  Charles  P.  Steinmetz 


z=  Vr2+x2 

t  an  a  =  - 
r 

r= resistance  of  circuit. 

x  =  reactance  of  circuit. 

p= frequency  ratio  of  beat  or  oscillation,  that  is, 

pf=  frequency  of  oscillation,  and 

E0= effective  value  of  machine  EMF. 

As  seen  from  the  equations,  during  each  complete  cycle  of  the 
oscillations,  of  frequency  pf,  the  current  i  twice  rises  and  falls,  thus 
reaching  two  maxima,  and  the  power  p  twice  reaches  a  maximum 
and  twice  reverses,  so  that  the  energy  W  flows  one  way  during  half 
the  cycle,  and  in  the  opposite  direction  during  the  other  half  cycle. 
The  frequency  of  the  rise  and  fall  of  the  current  thus  is  2  pf. 

Figure  1. — I  and  II  show  the  curve  i  and  voltage  ei  of  the  oscilla- 
tion, for  the  (exaggerated)  value  p  =  .l,  for  o>0=45  degrees  and 
wo  =  90  degrees. 

B 

Consider  now  the  case  that  two  alternators,  or  groups  of  alter- 
nators such  as  station  sections,  are  connected  together  while  different 
from  each  other  in  frequency  by  2s,  that  is,  one  alternator  has  the 
frequency  (1—  s)  f,  the  other  the  frequency  (1+s)  f. 

We  may  again  assume  the  alternators  as  of  equal  voltage,  since  a 
voltage  difference  merely  superposes  on  the  synchronizing  energy 
current  a  reactive'magnetizing  current,  without  materially  changing 
the  energy  relations. 

The  EMFs  of  the  two  alternators  then  may  be  represented  by: 

CI=E  cos  (i— s)j<£  \ 

e2  =  E  cos  (1+s)  <t>  J  (9) 

The  resultant  voltage  in'the  circuit  between  the  two  alternators  then  is : 
e  =  ei— e2 

=  E<cos  (1  — s)  <p  —  cos  (1+s)  <f>\ 

=  2E  sin  s0  sin  <£  (10) 

[Assumingjnow  that  s  is  a  small  quantity  (just  as  we  assumed  in 
A,  that  p  is  a^small  quantity),  that  is,  that  the  two  alternators  have 
nearly  the  samejfrequency.  The  change  of  sin  s<£  then  is  slow  com- 
pared with  that  of  sin<£,  and  for  all  phenomena  of  the  frequency  f, 
sin  s<j>  may  be  assumed  as  constant,  and  the  reactance  of  the  circuit 


Report  of  Charles  P.  Steinmetz  27 

may  be  assumed  as  the  same,  x  =  27rfL,  for  both  component  EMFs, 
ei  and  e2  that  is,  for  both  frequencies  (1  —  s)  f  and  (1+s)  f.] 

The  interchange  current  between  the  alternators  then  is: 

i  =  —  sin  s<t>  sin  (0  —  a) 

z  . 

where: 


z=  Vr2+x2 

tana=-  (11) 

With  regards  to  the  EMF  of  one  of  the  alternators,  for  instance, 
ei  this  current  always  lags.  Its  lag  is  90  degrees  when  the  current  is 
a  maximum.  With  decrease  of  current,  the  lag  decreases  from  90 
degrees  in  the  one,  and  increases  in  the  next  beat,  and  approaches  in 
phase  respectively  in  opposition,  when  the  current  is  a  minimum. 
The  power  factor  thus  varies  from  zero  at  maximum  current,  to 
unity  at  zero  current,  and  its  average  thus  is  low.  Fig.  1  shows  as 
Curve  III  the  relation  of  ei  to  i  for  the  exaggerated  values  s  =  .09. 

The  power  of  one  of  the  two  alternators  then  is  given  by : 

2F"2 

=  —  -  sin  s<£  sin  ($  —  a)  cos  (1  — s)  <f> 

E2  f  | 

=  —  sin  s0  <  sin  [(2  — s)  <f>  —  a]+sin  (s<£  —  a)  > 
z  I  J 

TT2  TT2  TT2 

=  —  sin  0  sin  [(2  — s)  <4  —  a]-}-s-  cos  a  —  ^-  cos  (2sd>  —  a) 
z  2z  2z 

The  first  term  again  is  the  double  frequency  term  representing 
the  energy  storage  by  inductance;  the  second  term  is  the  power 
consumed  by  the  resistance  of  the  circuit.  Neither  thus  represents 
energy  transfer  between  the  alternators. 

The  third  term : 

E2 
(sj,_  \  (i2\ 

is  a  slow  pulsation  of  energy,  which  alternately  accelerates  the 
machine  and  thus  tends  to  bring  it  nearer  to  synchronism,  and  then 
retards  it  again. 

Usually,  it  is  approximately:  a  =  90  degrees,  that  is,  the  reactance 
is  large  compared  with  the  resistance,  and  equation  (12)  then  be- 
comes : 


28  Report  of  Charles  P.  Steinmetz 

E2 

p  =  2^sin2s<£ 

During  each  cycle  of  the  frequency  sf,  of  the  slip  from  synchro- 
nism or  average  frequency,  the  amplitude  of  the  current  i  thus  twice 
becomes  zero  and  in  phase,  and  twice  reaches  a  maximum,  when  the 
alternators  are  in  opposition,  and  the  power  p  four  times  reaches  a 
maximum  and  four  times  becomes  zero  and  reverses,  twice  when 
the  current  comes  into  phase  with  the  EMF,  but  the  current  becomes 
zero,  and  twice  when  the  current  is  a  maximum,  but  in  quadrature 
with  the  EMF,  and  the  power  thus  becomes  zero.  The  power 
transfer  between  the  alternators  thus  reverses  four  times  per  com- 
plete cycle  of  slip,  sf,  that  is,  is  of  the  frequency  2sf,  with  two  positive 
and  two  negative  maxima. 

The  average  value  of  the  power  is: 

2   =Ef 

7T  7TZ 

and  as  the  duration  of  one  quarter  cycle  of  slip  is  t  =  j-p,  the  energy 

transfer  between  the  two  machines,  during  a  quarter  cycle  of  slip 
thus  is: 

1   2 


-S55 

There  is  thus  that  difference  between  the  slipping  of  alternators 
past  each  other  out  of  synchronism,  and  the  oscillation  of  the  alter- 
nators against  each  other  at  synchronism  (A),  that  in  the  slipping 
the  power  fluctuation  and  the  reversal  of  the  energy  is  of  twice  the 
frequency  of  the  current  fluctuation,  while  in  the  oscillation  of  the 
alternators  against  each  other  at  synchronism,  the  power  fluctuation 
or  reversal  of  energy  flow  is  of  the  same  frequency  as  the  current 
fluctuation. 

If  two  alternators  are  connected  together  while  out  of  synch- 
ronism, and  slowly  slip  past  each  other,  during  each  half  cycle  of 
slip,  or  beat,  while  the  two  machines  EMF  pass  from  in  phase  to  in 
opposition  to  in  phase  again,  a  periodic  energy  transfer  takes  place. 
During  one  quarter  cycle  of  slip  (that  is,  while  one  alternator  EMF 
slips  behind,  the  other  pulls  ahead  of  the  minimum  frequency  by 
one  quarter  cycle,  and  the  two  alternator  EMFs  thus  slip  against 


Report  of  Charles  P.  Steinmetz  29 


each  other  by  one  quarter  cycle),  the  alternators  are  partly  in  phase 
with  each  other,  and  the  slower  machine  receives  energy  from  the 
faster  machine.  The  two  machines  are  thereby  brought  nearer  to 
each  other  in  speed,  pulled  towards  synchronism.  During  the  next 
quarter  cycle  of  slip,  however,  the  two  alternators  are  partly  in 
opposition,  and  the  faster  machine  receives  energy  from  the  slower 
one.  The  faster  machine  then  speeds  up,  the  slower  machine  slows 
down,  and  the  two  machines  pull  apart  again,  by  the  same  amount 
by  which  they  pulled  together  in  the  preceding  quarter  cycle  of  slip 
(if  their  EMF  is  constant).  Thus  the  two  machines  can  pull  into 
step  only  if  the  energy  transferred  during  one  quarter  cycle  of  slip, 
W,  is  larger  than  the  energy  required  to  speed  up  the  momentum  M 
of  the  machine,  to  full  synchronism. 

Due  to  the  energy  transfer  W  between  the  machines,  resulting 
in  an  alternate  speeding  up  and  slowing  down,  the  slip  s  is  not  con- 
stant, but  pulsates  periodically,  between  the  minimum  value  s—  Si, 
at  the  end  of  the  quarter  cycle  during  which  the  machines  pull 
together,  and  beginning  of  the  quarter  cycle  during  which  the 
machines  pull  apart,  and  a  maximum  value  s+Si,  at  the  end  of  the 
quarter  cycle,  during  which  the  machines  pull  apart,  and  beginning 
at  the  quarter  cycle  during  which  the  machines  pull  together  —  where 
Si  is  the  amplitude  of  the  pulsation  of  slip.  As  the  energy  required 
to  accelerate  the  momentum  M  of  the  machine  by  the  speed  2s  i  is 
4s  jM,  it  follows: 


W 
E2 


l     167rsfzM 

is  the  amplitude  of  the  speed  fluctuation  of  the  two  alternators 
during  their  slipping  past  each  other,  out  of  synchronism  with  the 
slip  s. 

Si  =  s  gives  the  minimum  slip  s  —  Si  =  0,  that  is,  the  machines  pull 
into  synchronism. 

The  maximum  slip  Si  from  which  the  two  machines  pull  into 
synchronism  with  each  other,  thus  is  given  by  substituting  si  =  s 
in  (14),  as: 

E 

So= 


30  Report  of  Charles  P.  Steinmetz 

So  thus  is  the  limit  of  synchronizing  power. 

Substituting  again  the  effective  value  of  EMF,  E0,  for  the  maxi- 
mum value  E,  by: 
JR 

Eo=V2 
gives  the  effective  values: 

Resultant  voltage: 

e°  =  2E0sins4>  (10l) 

Current: 

2F" 

io  =  ^-sins<£  (Hi) 

z 

Power  transfer: 

p  =  —  cos  (2s0-a)  (121) 

X 

Energy  transfer  during  one  quarter  cycle  of  sUp: 


Amplitude  of  pulsation  of  slip: 


Critical  Slip,  from  which  the  machines  pull  each  other  into  synchro- 
nism, or  limits  of  synchronizing  power: 


These  expressions  are  very  similar  to  those  of  A,  with  s<£  taking 
the  place  of  «,  and  2s  the  place  of  p. 

C 

With  two  machines  out  of  synchronism  with  each  other  by  a 
greater  speed  difference  2s,  than  that,  from  which  the  machines  can 
pull  each  other  into  synchronism  within  one  quarter  cycle  of  slip, 
from  the  equations  of  B  it  would  follow,  that  the  machines  can  never 
pull  each  other  into  synchronism,  if  the  voltage  E0  is  constant,  but 
must  indefinitely  continue  to  slip  past  each  other,  coming  nearer 
together  during  one  quarter  cycle  of  slip,  and  dropping  apart  again 
by  the  same  amount  during  the  next  quarter  cycle  of  slip. 

This,  however,  is  under  the  assumption,  that  the  machine  EMF 
E0  is  constant.  In  reality,  however,  E0  is  not  constant,  but  varies 
periodically  with  the  same  frequency  as  the  current  fluctuates.  The 


Report  of  Charles  P.  Steinmetz  31 


current  in  the  circuit  between  the  machines  and  thus  the  armature 
reaction  in  the  machine  varies  in  amplitude  and  in  phase  difference 
against  the  machine  voltage,  and  the  machine  voltage  varies  with 
the  amplitude  and  the  phase  of  the  armature  reaction. 

Consider,  as  approximation,  the  armature  reaction  as  propor- 
tional to  the  quadrature  component  of  the  current.  The  EMF  of 
the  machine  would  then  be  expressed  by  an  approximate  equation  of 
the  form: 

E  =  E0  |  1— c  sin  s<£  sin  <f>  \ 

where  <f>  is  the  phase  angle  between  the  current  and  the  EMF  and 
sins0  represents  the  amplitude  of  the  current  pulsation,  by  (II1) 

it  is,  however,  by  (9)  and  (11): 

<p=(<f>— a)  —  (1  —  s)  0  —  90  degrees 

=  s0  —  a +90  degrees 
thus: 

f  1 

E  =  E0  |  l+c  sin  s0  cos  (s0  — a)  j>  (16) 

Substituting  (16)  into  the  expression  of  the  power  of  the  alter- 
nator (12 x),  the  equations  still  remain  alternating,  that  is,  there  is 
no  resultant  synchronizing  power,  but  equal  positive  and  negative 
values  of  power  alternate. 

However,  (16)  assumes  that  the  magnetizing  effect  of  the  armature 
reaction  is  instantaneous,  that  is,  that  the  EMF  E  at  any  moment 
is  the  value  corresponding  to  the  armature  reaction  existing  at  this 
moment.  This,  however,  is  not  the  case,  and  the  armature  reaction 
is  not  instantaneous,  but  requires  an  appreciable  time,  several 
seconds,  to  develop,  and  the  magnetizing  or  demagnetizing  effect  of 
the  armature  reaction  on  the  voltage  therefore  materially  lags  behind 
the  armature  reaction. 

Let  then  a  =  angle  of  lag  of  the  voltage  change  behind  the  armature 
reaction  which  causes  it.  It  is  then — 

f  1 

E  =  E0{  l+c  sin  s0  cos  (s0-a  — <r)  \  (17) 

I  J 

and,  substituting  (17)  into  (121),  give  the  power  transfer  between  the 
machines : 

E2  f  1  2 

p=— -  cos  (2s0  =  a)  \  1+c  sin  s0  cos  (s0  —  a  —  a)  \ 
z 


32  Report  of  Charles  P.  Steinmetz 

or  approximately,  since  c  is  a  small  quantity: 

p  =  —  cos  (2s$  —  a)  -\ —    —  cos  (2s0  —  a)  sin  s$  cos  (s0  —  a  —  a) 
z  z 

The  first  term: 

E  2 

p'  =  -™  cos  (2s$  —  a) 

is  the  slowly  alternating  energy  transfer  between  the  machines 
which  causes  their  speed  to  fluctuate,  but  does  not  permanently 
bring  them  nearer  to  each  other,  that  is,  exerts  no  synchronizing 
power. 

The  second  term : 

p"  = cos  (2s0  — a)  sin  s<£  cos  (s<£  —  a  —  a) 

z 

f 
=  — -  cos  (2s0  —  a)  |  sin  (a 

-  sin  (a+o-)  cos  (2s0  — a)+^^-|sm(4s0  — 2a  — <r)  —  sina- 
The  first  two  terms  of  this  expression : 

TT    2 

sin  (a+a)  cos  (2s<£  —  a) 


sin   4s</>  — 2a  — 


z 
and 

cE02 
2z 

are  slowly  alternating,  thus  represent  no  permanent  acceleration, 
that  is,  no  synchronizing  power. 

The  third  term  however: 

cE02   . 
P°~2z~  Sm  *  '     ' 

is  constant,  that  is,  represents  a  continuous  synchronizing  power, 
which  steadily  pulls  the  machines  together,  until  their  speed  differ- 
ence 2s  has  become  small  enough  to  pull  the  machines  suddenly  into 
step. 

If  thus  two  alternators  or  station  sections,  are  considerably  out 
of  synchronism  with  each  other,  they  continue  slipping  past  each 
other,  with  large  fluctuating  currents  flowing  between  them,  and  the 
speeds  of  the  machines  fluctuating  with  the  fluctuation  of  the  current. 
These  currents  do  not  decrease  in  amplitude,  but  remain  of  practically 


Report  of  Charles  P.  Steinmetz  33 

constant  value,  but  their  period  of  fluctuation  gradually  gets  slower, 
that  is,  the  fluctuation  gradually  becomes  slower,  while  currents 
slowly  pull  the  machines  nearer  into  synchronism  with  each  other, 
that  is  decrease  their  frequency  difference,  until  the  critical  frequency 
2s0  is  reached  (where  the  acceleration  during  a  quarter  cycle  of  slip, 
2si,  reaches  full  synchronism.)  Then  the  machines  suddenly  drop 
into  synchronism,  but  oscillate  in  phase  against  each  other,  with  an 
approximately  constant  frequency  of  oscillation,  but  with  a  current 
fluctuation,  which  steadily  (and  usually  rapidly)  decreases,  until 
steady  conditions  of  speed,  current  and  voltage  are  reached. 

The  armature  reaction  of  the  alternator  is  represented  by  the 
difference  of  the  synchronism  reactance  x0  and  the  true  reactance  xi, 
that  is,  by  an  effective  reactance  of  armature  reaction. 

X2  =  Xo  —  Xi. 

The  co-efficient  c  in  the  synchronizing  power,  p0  (18),  is  that 
fraction  of  the  reactance  of  the  armature  reaction  x2,  which  appears 
during  the  short  time  of  the  current  fluctuation.  Thus  c  is  the  larger, 
the  slower  the  fluctuation,  that  is,  the  less  s.  In  other  words,  c 
increases  with  decreasing  slip,  that  is,  increasing  approach  to 
synchronism. 

Inversely,  a  is  a  maximum  and  practically  90  degrees  for  large 
values  of  s,  where  the  voltage  fluctuation  lags  practically  90  degrees 
behind  the  fluctuation  of  the  armature  reaction,  and  decreases  with 
decreasing  s,  that  is,  increasing  approach  to  synchronism,  c  sin  a 
and  thus  the  synchronizing  power  p0  (18),  thus  should  be  a  maximum 
at  some  moderate  slip  s,  and  decrease  for  larger  as  well  as  smaller 
sh'ps. 

Assuming  that  it  takes  to  seconds  for  the  field  to  build  up  to 
correspond  to  the  armature  reaction.  With  the  current  fluctuating 
with  the  frequency  2sf,  and  assuming  that  the  magnetizing  effect  of 
the  armature  reaction  is  sinoidal  which  at  best  is  but  a  very 
crude  approximation,  it  would  be: 

1 

~4sft0 
and: 


thus: 


34  Report  of  Charles  P.  Steinmetz 


However,  secondary  effects  occur  and  more  or  less  modify  the 
value  po  such  as  the  effect  of  secondary  currents,  induced  in  the 
field  structure  by  that  component  of  the  armature  current  which  is 
due  to  the  EMF  of  the  other  machine,  and  which  gives  an  induction 
motor  torque,  tending  to  pull  the  machines  together  into  synch- 
ronism. 

D 

Consider  two  alternators  or  groups  of  alternators  such  as  station 
sections  of  the  same  terminal  voltage,  connected  with  each  other 
through  an  impedance  z,  and  in  synchronism  with  each  other.  If 
then  the  load  distribution  between  the  alternators  differs  from  the 
distribution  of  their  driving  power,  electric  power  is  transferred  over 
the  impedance  z,  current  flows  and  a  phase  displacement  2co  occurs 
between  the  two  sides  of  the  reactor  z. 

In  this  case,  the  phase  angle  w  is  constant,  and  not  periodically 
fluctuating  as  in  A,  but  varies  with  changes  of  distribution  of  load ; 
the  equations,  however,  are  the  same  as  in  A,  except  that  now  w  is 
constant,  and  the  voltages  ei  and  e2  are  the  terminal  voltages. 

It  thus  is, 

Current  in  the  impedance: 

2E  . 

1  =  — sm  a)  sm  (<£  —  a) 

JE 

Voltage  across  the  impedance: 
e  =  2E  sin  co  sin  <£ 

Power  transferred  over  impedance: 

E2 
P  =  2~  tcos  a  — cos  (2co  — a)] 

where  E  is  maximum  value  of  the  terminal  voltages: 

CI=E  cos  (</>— w) 

e2  =  E  cos  (0+w) 
and  a  the  phase  angle  of  the  impedance. 

If  the  impedance  z  is  a  reactance,  that  is,  the  resistance  r,  is 
negligible:  r  =  0,  it  is  a  =  90  degrees,  and: 

2E    . 

i  = sm  o>  cos  <(> 

x 

e  =  2E  sin  co  sin  <£ 

E2  •    « 
=      sm 


Report  of  Charles  P.  Steinmetz  35 

or,  substituting  the  effective  values:    E  =  E0  V2: 

2E0   . 
ID  =  -  sin  w 

e°  =  2E0  sin  w 

p=—  —  sin  2w 
x 

The  power  p  thus  is  zero  for  co  =  0,  increases,  reaches  a  maximum: 
E  2 

Dm  —— 

X 

for  w  =  45  degrees,  or  90  degrees  phase  displacement  between  the 
Iternators,  and  then  decreases  again  to  zero  at  w  =  90  degrees,  or 
opposition. 

At  maximum  power  transfer,  it  is: 

E0  V2 


_ 

1m  — 


=  E0   V2 


E 

The  foremost  difficulty,  and  uncertainty  in  the  application  of 
the  preceding  equations,  is  found  in  the  selection  of  the  proper  values 
of  the  machine  EMF  E0.  E0  is  not  the  terminal  voltage;  by  slipping 
past  each  other  without  external  impedance,  the  terminal  voltage  of 
the  alternators  goes  down  to  zero.  Neither  is  E0  the  "nominal 
induced  voltage,"  as  this  has  no  actual  existence,  but  is  the  voltage 
which  would  be  induced  by  the  field  excitation  if  the  saturation 
curve  of  the  machine  continued  as  a  straight  line.  It  appears  to  me 
that  E0  must  be  considered  as  the  actual  induced  voltage,  that  is, 
the  voltage  induced  by  the  actual  field  flux,  that  is,  the  field  flux 
due  to  the  resultant  of  field  excitation  and  armature  reaction.  The 
armature  reaction,  however,  fluctuates  with  the  current  between 
zero  and  a  maximum,  while  the  actual  field  flux  is  practically  con- 
stant, since  the  magnetic  field  cannot  follow  the  relatively  rapid 
fluctuation  of  armature  reaction. 

The  magnetic  effect  of  the  armature  reaction  is  represented 
electrically  in  the  synchronous  reactance  XQ.  The  synchronous 
reactance  thus  consists  of  a  true  self-inductive  reactance  Xi,  which 
is  instantaneous,  and  an  effective  reactance  of  armature  reaction  x», 


36  Report  of  Charles  P.  Steinmetz 

which  requires  appreciable  time  to  develop,  and  does  not  correspond 
to  any  real  magnetic  flux. 


In  turbo-alternators,  x2  usually  is  very  much  larger  than  xi. 

Electrically,  the  actual  induced  EMF  thus  should  be  the  nominal 
induced  voltage  e0,  which  corresponds  to  the  field  excitation,  less 
the  reactance  drop  of  the  average  current  in  the  effective  reactance 
of  armature  reaction,  x2. 

If  then  I  =  maximum  effective  value  of  the  fluctuating  current, 

the  average  current  is  ~,  and  the  actual  induced  voltage  thus  is: 

m 


0  =   0  —  ~- 

It  is,  however,  in  two  alternators  connected  together  out  of 
synchronism,  through  an  additional  reactance: 

2E0=I  (2Xl+x) 

where  x  is  the  additional  reactance  through  which  the  alternators  of 
actual  induced  voltage  E0  and  true  self-inductive  reactance  Xi  are 
connected  together,  while  running  out  of  synchronism  with  each 
other. 

From  these  two  equations  fellows: 

Maximum  (effective)  value  of  the  fluctuating  interchange  current: 

(20) 
(21) 


9    _ 

2xx+x2+x 

and,  actual  induced  voltage: 


where  e0  =  nominal  induced  voltage,  effective  value. 

If  the  alternators  are  connected  through  an  impedance  z,  z  takes 
the  place  of  x,  combining  vectorially  with  xi  and  x2. 

In  this  calculation,  the  armature  reaction  has  been  assumed  as 
demagnetizing,  and  the  impedance  voltage  therefore  subtracted  from 
the  nominal  induced  voltage.  This  appears  correct,  as  the  inter- 
change current  between  the  alternators  out  of  synchronism  with 
each  other,  is  essentially  a  lagging  current,  throughout,  as  illustrated 
in  Fig.  1. 

If  the  two  alternators  are  in  synchronism,  but  out  of  phase  with 
each  other  by  a  maximum  phase  displacement  angle  2co0,  it  is: 

2E0sin  o>0=I  (2 


Report  of  Charles  P.  Steinmetz  37 

and,  again  assuming  the  armature  reaction  as  demagnetizing: 

v  Ixi 

^0=60 — n~ 

thus:    the  maximum  (effective)  value  of  the  fluctuating  exchange 
current: 


2xi-f  x+Xj  sin  w0 
and,  actual  induced  voltage: 

E^XI+X  ._.. 

o    eo  "~ * i.***/ 

where  eo  is  the  nominal  induced  voltage,  effective  value. 

However,  in  this  case  of  alternators  in  synchronism  but  oscillating 
against  each  other,  at  least  for  small  and  moderate  values  of  w0  the 
interchange  current  I  is  essentially  an  energy  current  with  regards 
to  the  machine  voltage,  and  the  reactive  component  of  this  current 
alternately  changes  between  lag  and  lead,  that  is,  between  demagnet- 
izing and  magnetizing.  Therefore,  the  correctness  is  doubtful  of 
subtracting  the  impedance  voltage  from  the  nominal  induced  voltage 
to  get  the  induced  voltage,  but  it  would  be: 

E0=  Ve0!-i2x22 

and  as  i  varies  between  0  and  I,  the  average  of  E0  would  be  the  mean 
between  e0  and   Ve02— I*xjJ,  thus: 
combining  with  the  equation: 

2Eo  sin  wo  =  I  (2xx+x) 
gives: 

T_  2e0  (2xi+x)  sin  w0 
~(2x,+x)2-fx32sin2w0 

E  (2xi+x)' 

°(2xi+x)2-|-x22  sin2w0 

It  is  probable  that  the  true  value  of  E0  lies  between  (23)  and 
(25),  but  nearer  to  (25). 

Substituting  these  values  (21),  (23),  (25)  into  the  equations  of 
A,  B  and  C,  and  substituting 

in  these  equations,  as  the  impedance  of  the  circuit  between  the  two 
alternators,  gives  the  equations  tabulated  in  F. 

The  nominal  induced  EMF  e0  is  derived  by  combining  the 
terminal  voltage  e  with  the  impedance  voltage  iz,  where  z  is  the  total 


38  Report  of  Charles  P.  Steinmetz 

impedance  inside  of  the  terminals,  true  reactance  as  well  as  effective 
reactance  of  armature  reaction.  For  non-inductive  load — and 
synchronous  machine  load  may  be  assumed  as  approximately  non- 
inductive — this  gives: 


=  Ve2+(ix) 


=  e   Vl+£2  (26) 

where  £  is  the  percentage  reactance,  and  the  resistance  is  neglected, 
as  small  compared  with  the  reactance. 

However,  this  expression  neglects  the  change  of  reactance  with 
increase  of  magnetic  saturation,  increase  of  magnetic  leakage  be- 
tween field  poles,  etc.,  and  therefore,  especially  hi  turbo-alternators 
with  their  enormous  magnetic  fields,  high  saturation  and  high  field 
leakage,  this  expression  is  not  very  accurate,  and  reasonably  reliable 
only  in  the  mean  range  of  current  and  voltage. 

In  B,  and  C,  the  case  of  two  alternators,  or  groups  of  alternators 
out  of  synchronism  with  each  other,  the  equations  of  synchronizing 
power,  energy  and  critical  slip  :  p,  p0,  W,  S0,  contain  the  term 

2xi+x 
2xi+x+x2 

thus  are  a  maximum,  if  this  term  is  a  maximum.    This  is  the  case  if: 

x2  =  2xi+x,  or 
x  =  x2  —  2xi 
that  is: 

The  synchronizng  power  between  alternators  out  of  synchronism 
with  each  other  is  a  maximum,  and  the  frequency  difference  from 
which  they  pull  each  other  into  synchronism,  is  greatest,  if  the 
alternators  or  group  of  alternators  are  connected  together  through  a 
reactance  which  is  equal  to  the  effective  reactance  of  armature 
reaction,  less  twice  the  self  inductive  reactance  of  the  circuit  between 
the  alternators  or  groups  of  alternators.  With  two  alternators  or 
groups  of  alternators  connected  together  without  any  external 
reactance,  this  means,  if  the  self  inductive  reactance  of  the  alternators 
or  group  of  alternators  is  one-third  the  synchronous  reactance.  With 
turbo-alternators,  the  self  inductive  reactance  usually  is  much  less, 
and  with  such  machines  the  synchronizing  power  thus  is  increased 
by  the  insertion  of  external  reactance. 

Substituting  above  relation  into  the  equations  of  B,  and  C,  gives 
as  the  expressions  for  the  case  of  maximum  synchronizing  power: 


Report  of  Charles  P.  Steinmetz  39 


Actual  machine  EMF: 

Resultant  EMF :  e°  =  e0  sin 

en  sin  i 
Resultant  current:  io  = 


Power  fluctuation  of  low  frequency :   p  =  — ~ — - — — 

4X2 

e  2 

Energy  transfer  of  low  frequency :       W  = 


r>     *  •  f  T-* 

Contmuous  power  transfer :  P0 = 

Critical  slip :  s0= 


a 

cep2  sin  a 
8  Xj 

So 


4  V27rfx2M 


40 


Report  of  Charles  P.  Steinmetz 


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Report  of  Charles  P.  Steinmetz 


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Report  of  Charles  P.  Steinmetz 


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Report  of  Charles  P.  Steinmetz  43 

Denotations 

e0=  nominal  induced  E.  M.  F.  of  alternator  or  group  of  alternators. 

Xii  =  true  self  inductive  reactance  of  alternator  or  group  of  alter- 
nators. 

xn=  external  reactance  of  alternator  or  group  of  alternators,  thus. 

Xi  =  xn+Xi2  =  total  self  inductive  reactance  of  alternators  or  group 
of  alternators. 

xj  =  effective  reactance  of  armature  reaction  of  alternator  or  group 
of  alternators,  thus: 

Xo=xn+x2  —  synchronous    reactance    of   alternator    or    group  of 
alternators. 

x  =  reactance  (or  impedance)  between  alternators. 

z  =  impedance  of  circuit  between  alternators. 

=  Vi-2+(2x!+x)2,  where 

r  =  resistance  of  circuit  between  alternators.     Or   approximately 


a  =  phase  angle  of  circuit  between  alternators,  where: 
tan   a  =  —  Or  approximately  : 

a  =  90  degrees. 

w  =  phase  displacement  from  mean,  of  oscillating  alternators,  thus: 
2co  =  total  phase  displacement  of  oscillating  alternators  from  each 

other. 

oj0  =  maximum  phase  displacement  during  oscillation. 
woo  =  initial  value  of  w0 
pf=  frequency  of  oscillation. 

s  =  slip  of  frequency  from  mean,  thus  : 
2s  =  slip  of  frequency  of  alternators  from  each  other,  and 
sf=  frequency  of  slip  from  synchronism; 
2sf=  frequency  of  slip  of  alternators  from  each  other. 
f=  synchronous  frequency. 

to  =  time  required  for  magnetizing  effect  of  armature  reaction. 
M  =  momentum,  in  joules,  of  alternator  or  group  of  alternators,  per 

phase,  that  is: 
3M  =  total  momentum. 


44 


Report  of  Charles  P.  Steinmetz 


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Report  of  Charles  P.  Steinmetz  45 

H 

In  the  trouble  of  September  18th,  1919,  the  following  machines 
were  involved  : 

In  Fisk  B  and  Northwest  Station  : 

123,000  KW  rating,  105,000  KW  load  =  85.5% 

In  Fisk  A  and  Quarry  Street: 

114,000  KW  rating,    90,000  KW  load  =  79% 
It  was: 

Fisk  A: 

Six  12,000  KW;  98%  reactance.     79%  load.    Thus: 

Vl+.79x.982=  1.265 

e0=1.265    x    5200  =  6600V.     x2  =  5.76;        Xl=.  458  +.405  =  863; 
M  =  50xl06. 

Quarry  St.  : 

Three  14,000  KW:    91%  reactance.     79%  load.     Thus: 

Vl+.79x.912=1.23. 
e0=6400V.     x2=4.60:  Xl  =  .318+.347  =  .665;  M  =  67xlO«. 


FiskB: 

Four  12,000  KW;     98%  reactance.     85.5%  load.     Thus: 

Vr+.8552x982  =  1.305. 
e0  =  6770V.     One  25,000  KW  was  immediately  shut  down. 

Northwest  Station: 

One  20,000  KW:     134%  reactance,  and  one  30,000  KW:    125% 

reactance. 

85.5%  load. 

20,000  KW:      Vl-f.8552x  1.342=1.52.     e0  =  7900V. 
x2  =  4.95;  Xl=.325+.168  =  .493;  M  =  78xl06. 


30,000  KW:      Vl  +  ,8552  x  1.252  =  1.46:     e0  =  7600  V. 
x2  =  2.99:          Xl  =  .214+.168  =  .382:  M  =  87xl06. 

Busbar  reactors  :     x  =  1.75 
Tie  cables  x  =   .074      r  =  .312. 

(1.)  Assuming,  at  first,  that  the  two  machines  in  Northwest 
Station  are  in  sychronism  with  each  other,  and  the  four  machines  in 
Fisk  B  are  in  synchronism  with  each  other,  but  that  Fisk  B  is  out 
of  synchronism  with  Northwest  Station.  It  is  then,  in  the  circuit 
between  Fisk  B  and  Northwest  Station: 


46  Report  of  Charles  P.  Steinmetz 

Nominal  induced  EMF,  average: 
e0  =  7250  V. 

Actual  induced  EMF: 
E2  =  . 263  e0=  1910  V. 

Terminal  voltage,  average: 

Et  =  .77E0=1470  V.        EtV3  =  2550V. 

Current  between  stations,  maximum  effective  value: 
io  =  6400  A. 

Max.  pulsating  power,  per  phase: 
p  =  6150KW. 

Max.  steady  power  transfer,  per  phase : 
p0  =  770KW. 

Critical  slip : 

so  =.77%;  So1  =  .70%;  So+So^l.47% 

These  values  do  not  well  agree  with  the  observations  recorded, 
and  while  so  many  assumptions  had  to  be  made  in  the  calculations 
that  the  exact  numerical  values  can  not  be  relied  upon  too  closely, 
nevertheless,  the  general  magnitude  of  the  numerical  values  can 
generally  be  relied  upon.  It  is  probable  that  a  terminal  voltage  of 
2550  would  not  have  escaped  notice  in  the  indicating  meter ;  a  slowly 
pulsating  power  transfer  of  3p  =  18,450  KW  would  have  shown  on 
the  record  as  a  bad  fluctuation,  while  the  record  shows  an  apparently 
steady  flow  of  about  1000  KW  only.  Also,  the  fluctuating  inter- 
change current  between  the  stations,  rising  to  6400  amperes,  would 
probably  have  shown  marked  distress  in  the  cable. 

It  must  therefore  be  assumed  that  the  generators  in  the  same 
stations  did  not  stay  in  synchronism  with  each  other,  and  more 
particularly  that  the  20,000  and  the  30,000  KW  unit  in  Northwest 
Station  broke  out  of  synchronism.  The  behaviour  of  these  machines, 
as  the  gradual  loss  of  the  field,  is  an  indication  in  the  same  direction. 
(2.)  With  the  20,000  and  the  30,000  KW  units  of  Northwest 
Station  out  of  synchronism  with  each  other  on  the  busbars  the 
following  relations  would  be  obtained : 

x,  =  3.97;  2x!  =  .875  =  z;  M!  =  78xl06;  M2  =  87xl06. 
e0  =  7750  V. 
E0=.  181  e0=  1400  V. 
io  =  3200  A. 
p  =  2230KW. 
So=.68%         so1  =.64%         so+xo^l.32% 


Report  of  Charles  P.  Steinmetz  47 

Thus  with  the  breaking  of  the  synchronism  between  these 
machines,  the  voltage  and  the  circulating  current  materially  dropped, 
and  with  it  also  the  current  circulating  between  these  machines  and 
Fisk  B. 

The  30,000  KW  machine  then  was  shut  down,  leaving  the  20,000 
KW  as  the  only  unit  in  Northwest  Station,  drafting  out  of  synchro- 
nism with  Fisk  B.  Assuming,  however,  that  the  four  12,000  KW 
units  in  Fisk  B  have  kept  in  synchronism  with  each  other,  the  rela- 
tions obtained: 

(3.)  One  20,000  KW  unit  in  Northwest  Station;  four  12,000  KW 
units  in  Fisk  B  in  synchronism  with  each  other,  but  the  two  stations 
out  of  synchronism  with  each  other : 

x2  =  3.20:    2Xl=.709:    x=.074:    r  =  .312:    z  =  .84:    1^  =  78  xlO6: 
M2  =  200xl06. 
e0=7330  V. 
E0=. 208  e0=  1520  V. 

Et  =  .69  Eo  =  1050  V.  Et  V3  =  1820  V. 

io  =  3600  A. 
p  =  2750  KW. 
so -.75%:         so1  =  .47%         80+80*  =  1.22%. 

While  the  values  of  p  and  i0  are  much  lower  than  in  (1),  still  they 
are  much  larger  than  indicated  by  the  records;  3600  A.  maximum 
effective  value  of  interchange  current  would  give  a  loss  in  resistance 

3  rin2 
of  the  tie  cables  of  '—=—  =  600  KW,  in  addition  to  the  fluctuating 

Zi 

power  reaching  a  maximum  of  3p  =  8250  KW. 

Assuming  then  that  not  only  the  two  stations,  Fisk  B  and  North- 
west, but  also  the  individual  generators  in  either  station  had  broken 
synchronism.  The  conditions  then  pertain: 

(4.)  Two  12,000  KW  alternators  in  Fisk  B  out  of  synchronism 
with  each  other: 

x2  =  5.76:     2x!  =  1.726  =  z:     M  =  50xl06. 
e0  =  6770  V. 

E0=.23  63  =  1560  V.        Eo  V3~=  2700V. 
io=1820  A. 
p=1410KW. 
s0=.67%        2s0=1.34% 

(5.)  The  20,000  KW  unit  in  Northwest  Station  against  one 
12,000  KW  unit  in  Fisk  Street,  B. 


48  Report  of  Charles  P.  Steinmetz 


x2  =  5.35:  2x!=1.356:  x  =  .074:  r  =  .312:  z  =  1.46:  M^SOxlO6: 
M2  =  78xl06. 

e0 = 7330  V. 
E0=. 215  e0=  1570V. 
Et  =  61  Eo = 950  V.        Et  =  V3  =  1640  V. 

io  =  2150  A. 

p  =  1690KW. 

s0=.73%.        so1  =  .59%  so+so^l.32% 

This  means,  with  all  the  alternators  in  Fisk  B  and  in  Northwest 
Station  out  of  synchronism  with  each  other,  the  terminal  voltage 
will  be  between  1640  and  nothing.  The  interchange  current  cir- 
culating between  them  will  reach  maximum  amplitudes  not  exceeding 
1820  to  2150  amperes  effective.  The  i2r  loss  in  the  tie  cables  then 
would  fluctuate  between  maximum  values  of  1500  to  2200  KW  and 
nothing,  with  a  probable  average  of  about  900  KW.  This  agrees 
with  the  observation  that  the  wattmeter  in  the  tie  lines  was  very 
steady  showing  about  1000  KW,  and  the  voltage  was  in  appreciable. 

The  conclusion  therefore  is  inevitable,  that  in  this  trouble,  not 
only  the  Northwest  Station  and  the  Fisk  Street  B  Station  had 
broken  synchronism  with  each  other,  but  that  the  individual  gene- 
ators  in  the  Fisk  Street  B  Station  and  in  the  Northwest  Station  had 
broken  synchronism  with  each  other  also,  and  were  drifting  past  each 
other  out  of  synchronism. 

The  important  question  then  is,  what  caused  these  alternators 
and  stations  to  break  synchronism. 

That  the  Northwest  Station  and  the  Fisk  Street  B  Station  drifted 
out  of  step  with  each  other  was  to  be  expected.  As  the  tie  cable 
which  connect  the  bus  bars  of  these  two  stations  with  each  other 
contain  appreciable  resistance  but  practically  no  reactance,  and  the 
synchronizing  power  depends  on  the  reactance,  there  can  be  only 
very  little  synchronizing  power  between  these  stations,  that  is,  in 
normal  synchronous  operations  of  these  two  stations,  it  is  the  in- 
dividual generators  of  one  station  which  synchronize  with  those  of 
the  other  station,  rather  than  the  stations  as  a  whole. 

However,  the  alternators  in  Fisk  Street  B,  have  considerable 
reactance,  and  no  resistance  between  each  other.  The  reason  for 
their  breaking  synchronism  with  each  other  must  be  found  in  the 
great  drop  of  voltage  resulting  from  the  break  of  synchronism  be- 
tween Fisk  Street  B  and  Northwest  Station.  The  synchronizing 


Report  of  Charles  P.  Steinmetz  49 

power  is  proportional  to  the  square  of  the  voltage.  With  Fisk 
Street  B  and  Northwest  Station  out  of  synchronism  with  each  other 
but  the  individual  alternators  in  either  station  still  in  synchronism 
with  each  other  (Case  1),  the  actual  induced  voltage  in  these  two 
stations  drops  to  an  average  of  E0=1910  volts  per  phase.  The 
synchronizing  power  between  two  machines,  for  instance,  two  of  the 
12,000  KW  alternators  of  Fisk  Street  B,  reaches  a  maximum  at  a 
phase  displacement  between  two  machines  of  2co  =  90  degrees,  and 
then  is: 

p  =  —  =  2100  KW  per  phase, 

or  a  total  of  6300  KW,  or  about  half  load,  and  still  less  in  (Case  3), 
after  the  30,000  KW  unit  had  been  shut  down. 

Thus,  if  the  load  is  suddenly  released  on  these  machines,  unless 
the  steam  supply  can  be  reduced  almost  instantly  to  less  than  half 
load,  these  machines  will  be  torn  out  of  synchronism  with  each  other. 
But  by  breaking  synchronism  between  machines  in  the  same  stations 
—as  the  20,000  and  the  30,000  in  Northwest  Station— the  voltage  is 
still  further  lowered  and  thereby  the  synchronizing  power  reduced, 
so  that,  if  one  machine  breaks  out  of  synchronism  under  these 
circumstances,  all  will  break.  This  must  have  happened  on  Sep- 
tember 18th,  1919.  In  other  words,  the  break  of  synchronism 
between  Fisk  Street  B  and  Northwest  Station  lowers  the  voltage  so 
that  there  is  not  sufficient  synchronizing  power  left  to  keep  the 
individual  machines  in  each  station  in  synchronism  with  each  other. 

The  important  question  then  arises,  what  is  the  minimum  machine 
voltage  necessary  to  assure  the  individual  machines  of  each  station 
to  remain  in  synchronism  with  each  other  irrespective  of  any  sudden 
release  of  full  load.  That  is,  at  what  voltage  does  the  synchronizing 
power  of  the  individual  machines  become  greater  than  full  load. 
This  is  gven  by: 

E02     1      .. 

P=— grating 

as  shown  in  the  following  table: 

TABLE 

Lowest  Voltage  at  Which   Machines  Stay  in  Synchronism, 
If  Full  Load  is  Thrown  Off 

Bating  of  Machine, 

KW 12,000  14,000  20,000  25,000  30,000  35,000 

Voltage  per  Phase, 

E0= 2,630  2,490  2,560  2,740  2,770  2,650 

Eo  V"= 4,560  4,500  4,430  4,750  4,810  4,600 


50  Report  of  Charles  P.  Steinmetz 

As  seen,  as  long  as  the  actual  induced  voltage  does  not  drop  below 
5000  volts  there  appears  no  danger  of  any  of  the  machines  breaking 
out  of  synchronism  with  the  other  machines  in  the  same  station. 

The  insertion  of  sufficiently  large  power  limiting  reactors  between 
Fisk  Street  B  and  Northwest  Station  would  in  case  of  these  stations 
breaking  synchronism  with  each  other,  maintain  sufficient  voltage 
in  these  stations,  so  that  the  machines  in  each  station  may  be  ex- 
pected to  keep  in  synchronism  with  each  other. 

Coming  now  to  the  consideration  of  the  relation  between  Fisk 
Street  B  and  Quarry  Street  Station,  during  the  trouble  of  September 
18th,  1919: 

(6.)  Four  12,000  KW  alternators  in  Fisk  Street  B,  out  of  synch- 
ronism over  a  power  limiting  reactor  with  three  14,000  KW  alter- 
nators in  Quarry  Street,  the  latter  in  synchronism  with  each  other: 

x2  =  1.48:     2Xl  =  .438:     x=1.75:     z  =  2.19:     Mi  =  200  x  106: 
M2  =  200xl06. 

e0  =  6585  V. 

Eo  =  .597  e0  =  3930  V.       E0  V3  =  6800  V. 

0  =  3500  V.      Et  V3  =  6000  V. 


io  =  3600  A. 
p  =  7000KW. 

So  =  s01  =  .76%  s+s0=1.52% 

As  seen,  in  Quarry  Street,  the  voltage  E0  V3  is  6800,  thus  well 
above  the  value  required  for  stability  of  synchronous  operation  of 
the  alternators  in  this  station,  and  no  danger  existed  of  their  breaking 
synchronism. 

The  record  shows  during  the  disturbance,  while  Quarry  Street 
was  connected  with  Fisk  Street  B  out  of  synchronism,  a  fairly  uniform 
sustained  voltage  of  6800,  preceded  by  an  initial  drop  of  short 
duration,  below  6000  volts.  The  latter  may  be  accounted  for  by  the 
feeding  back  from  Quarry  Street  over  the  substations  into  Fisk  B 
and  Northwest  Station,  which  pulled  the  voltage  of  Quarry  Street 
down,  until  the  substations  cut  off,  and  required  some  time  to  recover. 
The  above  calculated  voltage  of  6000  is  lower  than  the  observed 
voltage  of  6800.  However,  Quarry  Street  was  also  connected  to 
Fisk  Street  A,  and  the  latter  station  was  assisting  Quarry  Street  in 
feeding  the  current  over  power  limiting  reactor  B  into  Fisk  B  and 
Northwest  Station.  We  may  thus  estimate  the  effect  of  Fisk  A  in 
holding  up  the  voltage. 


Report  of  Charles  P.  Steinmetz  51 


(7.)  Four  12,000  KW  alternators  in  Fisk  B,  out  of  synchronism 
over  a  power  limiting  reactor  with  three  14,000  KW  alternators 
in  Quarry  Street,  the  latter  in  synchronism  with  each  other,  and  over 
a  second  power  limiting  reactor,  with  six  12,000  KW  alternators 
in  Fisk  A. 

.  x2=1.21:   2Xl  =  .414:   x=1.75:    z  =  2.16:   Mi  =  200  x  10«: 

M2=500x  106. 
e0  =  6635  V. 

Eo  =  .64  e0  =  4240  V.  E0  VT=  7350  V. 

Et  =  3800  V.  Et  V3  =  6600  V. 

io  =  3900  A. 
p  =  8300KW. 
so  =-82%. 

As  seen,  the  calculated  value  of  the  terminal  voltage  of  Quarry 
Street,  6600,  agrees  as  closely  with  the  observed  value  of  6800  V.  as 
can  be  expected  from  such  approximated  calculations,  especially 
when  considering  that  some  synchronous  machines  had  been  lost 
by  Quarry  Street  in  the  substations,  and  the  load  thereby  reduced, 
which  would  result  hi  an  increase  of  voltage. 

As  the  total  impedance  of  Fisk  Street  A  is  about  1.1,  and  it  is 
connected  to  Quarry  Street  by  x=1.75,  the  voltage  of  Fisk  Street  A 
should  be  higher  than  Quarry  Street  in  the  proportion  of  1.1  to 
1.1  +  1.75.  This  gives  for  Fisk  Street  A:  Et  V3  =  8100  V.  This  well 
agrees  with  the  average  of  the  voltage  record  of  Fisk  Street  A  during 
the  first  seven  minutes  of  the  disturbance. 

Allowing  for  the  continuously  low  voltage  maintained  at  Fisk 
Street  B  by  the  out  of  synchronism  condition  with  Northwest 
Station,  the  fluctuating  current  over  the  reactor  B  between  Fisk 
Street  B  and  Quarry  Street  would  vary  approximately  between  1200 
and  2700  amperes.  Assuming  a  temperature  rise  of  these  reactors 
of  30°C.  at  600  A.,  this  would  give  an  estimated  final  temperature 
rise,  at  this  excessive  overload,  of  600  to  800°C.,  so  that  it  should  be 
expected  that  after  seven  minutes,  when  this  reactor  was  discon- 
nected, it  would  be  very  hot. 

The  reactor  A,  between  Quarry  Street  and  Fisk  Street  A,  should 
carry  a  current  of  500  to  1000  amperes,  thus  would  not  become 
heated. 

The  conclusion  then  is :  As  the  calculated  numerical  values  agree 
with  the  records  of  observation  as  closely  as  can  be  expected  from 


52  Report  of  Charles  P.  Steinmetz 


such  necessarily  approximated  calculations,  it  appears  safe  to  accept 
the  correctness  of  the  explanation  that  — 

Fisk  Street  A  and  Quarry  Street  remained  in  synchronism  with 
each  other,  but  Fisk  Street  B  and  Northwest  Station  broke  out  of 
synchronism  with  Quarry  Street  and  with  each  other,  and  the 
individual  machines  of  these  latter  two  stations  broke  out  of  synchron- 
ism with  each  other,  and  were  unable  to  pull  into  step,  due  to 
frequency  differences  greater  than  permissible  by  the  small  syn- 
chronising power  existing  between  these  machines  at  the  low  voltage 
existing  due  to  the  break  of  synchronism  between  the  stations. 

I 

In  the  trouble  of  May  19th,  1919,  the  following  machines  were 
involved  : 

Fisk  A: 

Five     12,000    KW  =  60,000    KW.     Load    32,000    KW  =  53%: 
98%  Reactance. 


.532x.982  =  1.13  e0  =  5900V. 

x2  =  5.76:    Xl=.458+.405  =  .863:     M  =  50xlO«. 

Quarry  Street  : 

Four    14,000    KW  =  56,000    KW.    Load    35,000  KW  =  62.5%: 

91%  Reactance. 

Vl+.6252x.912  =  1.15  e0=6000V. 

x2  =  4.60:    Xl=.  318+  .347  =  .665:    M  =  67xlO«. 

FiskB: 

Three   12,000   KW   and   one   25,000   KW  =  61,000   KW.  Load 
45,000  KW  =  74%. 
98%:     >100%  Reactance. 

.742x.982=1.24  e0  =  6450V. 


Vl+.742x  1.202=1.30  e0  =  6750V. 

25,000,  estimated:    x2  =  4.0:    xi  =  .45:     M  =  85xlO«. 

Northwest  : 

Two  20,000  KW  and  one  30,000  KW  =  70,000  KW. 
Load50,OOOKW  =  71%. 

134%:     125%  Reactance. 


20,000:      Vl  +  .712x  1.342=1.38         e0  =  7170V. 
x2  =  4.95:    xi  =  .  325+.  168  =  .493;    M  =  78xl06. 


30,000:      Vl  +  .712x  1.252  =  1.34         e0=7000  V. 
x2  =  2.99:     Xl  =  .214+.168  =  .382    M  =  87xl06. 
Busbar  reactors  :    x  =  1.75 
Tie  cables:  x=   .074;    r=.312. 


Report  of  Charles  P.  Steinmetz  53 

Let  us  assume  at  first  that  these  stations  have  dropped  out  of 
synchronism  with  each  other,  due  to  the  trouble  in  Fisk  A,  and  are 
drifting  past  each  other,  and  calculate  by  the  preceding  equations 
for  this  condition  the  voltages  and  currents  in  the  different  stations, 
and  compare  them  with  the  recorded  values,  to  see  whether  this 
assumption  is  reasonable.  It  is  then: 

(1.)     Fisk  A  out  of  synchronism  with  Quarry  Street: 
x2  =  (1.15+1.15)^-2  =  1.15;    2x1  =  .173+.166  =  . 
x=1.75  z  =  2.09 

e0  =  5950V. 

E0  =  —  ?-  e0=.645e0=3840  V. 
z-f-x2 


Et  =          Eo  =  3530  V.  Et  V3~=  6100  V. 


(2.)     Quarry  Street  out  of  synchronism  with  Fisk  B  and  Fisk  A  : 
x2=(1.15+.61)-7-2  =  .88;    2Xl  =  .166+.087  =  . 
x  =  .875;    z  =  1.128 


E0=.564e0  = 
E«=3120V.  Et  V3  =  5400  V. 

io=6250  A. 

(3.)     Fisk  B  out  of  synchronism  with  Northwest  Station: 
x2=  (1.30+  1.36)  -=-2  =  1.33;  2Xl  =  .176+.150  =  .326;  x  =  .074; 
r  =  .312;  z  =  .507. 

e0=6830  V. 
E0=.276e0=1880  V. 
E»=1530  V.  Et  V3  =  2650  V. 

io=7400  A. 

For  the  reasons  discussed  before,  it  is  not  probable  the  individual 
machines  in  Fisk  B  and  Northwest  Station  would  stay  in  synchronism 
with  each  other.  As  the  relatively  high  terminal  voltage  recorded  in 
the  stations  shows  that  the  individual  machines  stayed  in  synchro- 
nism with  each  other,  the  case  thus  may  be  considered  of  Fisk  B  and 
Northwest  Station  in  synchronism  with  each  other,  but  out  of 
synchronism  with  Quarry  Street: 


54 


Report  of  Charles  P.  Steinmetz 


(4.)  Fisk  B  and  Northwest  Station  in  synchronism  with  each 
other,  but  out  of  synchronism  with  Quarry  Street : 

X2=  (.683+ 1.15)4- 2  =  .92;  2x!  =  .13+.166  =  .299;  x  =  1.75; 

z  =  2.05. 
eo- 6840V. 
E0=.69e0  =  4720'V. 
Et=4250  V.  Et  V3  =  7350V. 

io  =  4600  A. 

Herefrom  then  we  get  the  terminal  voltages  of  the  different 
stations : 

Fisk  A:  Quarry:  Fisk  B:  Nw.  St.: 

(1.)  All  4  stations  out 
of  synchronism : 
Calculated     ter- 
minal voltage. .  .        6100  5400  2650  2650 
Observed 

records 7800  to  8200     7900  to  8100     8300  to  8400     8400  to  8500 

8100  to  8500 
(2.)  Fisk  B  and  Nw. 

Station  in  synchronism: 

Calculated 6100  5400  7350  7350 

Observed 

records 7800  to  8200  7900  to  8100  8300  to  8400  8400  to  8500 

8100  to  8500 

As  seen,  the  calculated  values  are  uniformly  very  much  lower 
than  the  observed  values,  and  while  no  very  great  accuracy  can  be 
attributed  to  such  approximated  calculations,  the  difference  is  too 
great  to  be  accounted  for,  and  it  must  therefore  be  concluded  that  in 
this  trouble  none  of  the  stations  had  broken  synchronism,  but  all 
the  four  stations  had  kept  in  synchronism  with  each  other. 

Assuming  then  as  reasonable,  that  in  the  trouble  of  May  19th, 
the  four  station  sections  had  kept  in  synchronism,  the  question 
remains  to  account  for  the  great  drop  and  fluctuations  of  voltage, 
which  were  greatest  at  the  source  of  the  trouble,  Fisk  Street  A,  and 
decreased  towards  the  other  end  of  the  station  chain,  whether  due 
to  the  hunting  of  the  stations  against  each  other,  or  due  to  excessive 
load  of  lagging  current,  caused  by  starting  of  synchronous  machines, 
or  due  to  some  other  cause. 

Assuming  first,  that  the  voltage  drop  and  voltage  fluctuations 
was  due  to  the  simultaneous  starting  of  numerous  synchronous 
machines.  To  estimate  the  effect  thereof,  in  the  following  table  are 
given,  in  columns  (1)  to  (3),  the  recorded  voltages  of  the  four  stations: 


Report  of  Charles  P.  Steinmetz  55 

The  initial  minimum  and  the  final  minimum  towards  the  end  of  the 
disturbance,  and  the  average  fluctuation.  In  the  second  line  is 
given  the  average  phase  voltage,  that  is  terminal  voltage  divided  by 
V3.  Column  (4)  then  gives  the  average  drop  of  voltage;  column  (5) 
the  total  station  impedance,  true  reactance  as  well  as  effective 
reactance  of  armature  reaction.  As  we  have  to  do  here  with  a 
sustained  voltage  drop,  the  armature  reaction  comes  into  play. 
Column  (6)  then  gives  the  average  value  of  the  lagging  current  in 
each  station,  which  would  account  for  this  voltage  drop.  As  seen 
these  are  fairly  moderate  currents.  This  would  be  the  lagging  current 
drawn  from  the  stations  in  starting  the  synchronous  machines  in  the 
substations.  As  (practically)  all  the  synchronous  machines  in  Fisk 
A  had  dropped  out,  but  only  a  few  on  the  other  stations,  most  of  this 
lagging  load  would  be  on  Fisk  Street  A.  Assuming  then  that  half 
this  current  had  been  consumed  directly  from  the  stations,  the  other 
half  transferred  over  the  power  limiting  reactors  to  Fisk  Street  A. 
Column  (7)  would  then  give  the  average  lagging  current  consumed  in 
each  station,  and  Column  (8)  the  current  transferred  over  the  power 
limiting  reactors  between  the  stations,  to  the  next  station,  and 
Column  (9)  gives  the  load  on  each  station,  in  KYA.  As  Fisk  Street  A 
lost  a  load  of  about  32,000  KW  in  synchronous  machines,  a  load  of 
12,000  KVA  starting  current  of  these  synchronous  machines,  during 
eighteen  minutes,  does  not  appear  excessive,  and  the  lesser  values 
in  the  other  stations  also  appear  of  reasonable  magnitude.  The 
voltage  across  the  power  limiting  reactors,  in  Column  (10).  and  the 
phase  angles  between  the  stations,  in  Column  (11),  are  very  moderate: 
only  a  little  over  5  degrees  maximum  phase  displacement  between 
Fisk  A  and  Quarry  Street.  That  is,  the  strain  is  very  moderate, 
and  very  far  from  the  limits  of  synchronizing  power. 

Assuming  now  the  second  explanation,  hunting  of  the  stations. 
Column  (12)  then  gives  the  estimated  values  of  the  quadrature 
voltage  resulting  from  the  swing  of  the  machines,  which  would  be 
required  to  bring  about  the  observed  voltage  drop:  V52002— e2 
where  5200  is  the  normal  phase  voltage  of  the  stations,  and  e  the 
observed  phase  voltage.  The  total  phase  angle  of  swing  then  is 
given  as  2  a?1  in  Column  (13).  As  the  limits  of  synchronizing  power 
are  at  90  degrees  phase  angle,  and  the  maximum  estimated  phase 
angle  of  swing  is  30  degrees,  it  would  appear — if  this  explanation  is 
correct — that  the  stations  were  still  far  from  the  limits  of  their 
synchronizing  power,  that  is,  quite  stable.  Column  (14)  then  gives 
the  true  self  inductive  reactance  of  the  stations,  and  Column  (15) 


56  Report  of  Charles  P.  Steinmetz 


gives  two  values  of  the  surging  current  in  the  stations  resulting  from 
the  oscillations  of  the  machines.  The  lower  value  is  calculated  by 
the  total  station  impedance,  Column  (5),  the  higher  value  by  the 
self  inductive  impedance  Column  (14).  The  true  value  would  be 
intermediate,  probably  nearer  the  larger  figure,  as  the  period  of 
oscillation  is  too  fast  to  develop  more  than  a  small  part  of  the  effective 
reactance  of  armature  reaction. 

Either  of  the  two  assumptions  gives  values  of  magnitude  which 
are  reasonable  and  in  accordance  with  the  observed  data,  so  that  in 
the  absence  of  any  data  on  the  phase  angle  between  the  stations,  it 
is  not  possible  to  decide  which  is  the  correct  explanation.  It  must 
be  recognized,  however,  that  neither  of  the  two  explanations  is 
entirely  satisfactory,  as  either  fails  to  account  sufficiently  for  the 
excessive  heating  of  the  reactor  B  between  Quarry  Street  and  Fisk 
Street  B.  This  makes  it  the  more  desirable,  in  view  of  the  import- 
ance of  fully  understanding  the  phenomenon,  to  install  phase  angle 
indicators,  that  is  suitable  synchronoscopes,  in  all  the  stations,  and 
carefully  observe  them  in  case  of  any  trouble  in  the  system. 


Report  of  Charles  P.  Steinmetz 


57 


y,                     /O 
3j 

•^ 

Station 

OO               OO               OO               -  I 

^           co           o           co 

.r^    O           .1-^    O            .t^    O            .[^    O 
ro  O1         £v^  f^          ^  *^         J5J^  f^ 

Min.           *- 
o 

s 

coco       toco       t—  i  co       toco 
o  cn       o  *»       o  co       o  to 
0000 

o          o          o          o 

1 

"to 

1+         1+         1+         1+ 

to               t£*               CO               «-4 

o          o          o          o 

O              0              O              0 

Fluct.        * 

"co 

CO                CO                >£t                Cn 

to           co           vo           co 
o          o          o          o 
1+         1+         1+         1+ 

t—  i               tO               1—  "               i£* 
tO               CO               ~4               O 

0000 

Average 
Voltage 
Drop 
per  Phase 

S 

1—  i                  H-  '                 1—  '                  H-" 

cn           £*           co           co 

O              -J               HJ               tO 

Station 
Impedance 
Ohms. 

"en 

to           to           co           *». 

to              ON              CO              *» 

o          o          o          o 

n* 

Average 
Current 

3 

1—  i                h-"                 h->                00 

—                   ^o                   \^                   -  1 

o          o          o          o 

tr 

Current 
Consumed 

3 

t—               tO              ifk. 

M           K           Qo 

o          o          o 

?: 

Current 
Transferred 

S 

H-                (-*                tO                tO 

cn              CO              Os              O 
O              O              Cn              O 
O               O              O              0 

CO 

Average 
Load  KVA. 
1 

3 

—           -  1 

CO               tO              Cn 

cn            O            O 

H. 

React. 

VolU 

i—  i 

Co            cn 

0                CO 

0                         0 

to 

£ 

Phase 
Angle 

i—  • 
i—  i 

CO                VO                tO                CO 
O              cn              to              \O 

o          o          o          o 

cn 
to 

o 
o 

M 

9 

/—  -v 

1—  I 
^to 

to           to           to           co 

1—  '               >£*.               ^1                O 
o                 o                 o                 o 

to 
e_ 

Phase 
Angle 

i—  • 

CO 

I-'             1—  1             1—  1             (—  ' 
cn            **j            ON            ""-J 
O               ON               ON              CO 

X 

!-* 

1—  1                     H-  1                     1—  '                    (—  I 
tO  h-  '          OH-1          CO  1—  i          —  — 

Oto       cnco       »i-  -  j       o  co 
OO        OO        OO        OO 
OO        OO        OO        OO 

Tr 

M 

V\ 

W 

5 


58 


Report  of  Charles  P.  Steinmetz 


S8 

RARE 

6K 


